From the second edition (1989):
O.K., a., n., and v.
(əʊˈkeɪ) Also OK, o.k., ok. [App. f. the initial letters of oll (or orl) korrect, jocular alteration or colloq. pronunc. of ‘all correct’: see A. W. Read in Amer. Speech XXXVIII (1963), XXXIX (1964), etc.
From the detailed evidence provided by A. W. Read it seems clear that O.K. first appeared as a jocular alteration of the initial letters of all correct (i.e. orl korrect) in 1839, and that in 1840 it was used as an election slogan for ‘Old Kinderhook’ (see sense Ab). Thence by stages it made its way into general use. Other suggestions, e.g. that O.K. represents the Choctaw oke ‘it is’, or French au quai, or that it derives from a word in the West African language Wolof via slaves in the southern States of America, all lack any form of acceptable documentation.]

A. adj. a. Chiefly in predicative use or as int.: all correct, all right; satisfactory, good; well, in good health; also in phr. O.K. by (someone): acceptable to (that person); freq. used as an exclamation expressing agreement: ‘yes’, ‘certainly’, ‘all right’; also appended to a statement or declaration as a strong form of challenge or appeal in which affirmation or agreement is expected. Also as adv.

1839 C. G. Greene in Boston Morning Post 23 Mar. 2/2 He‥would have the ‘contribution box’, et ceteras, o.k.—all correct—and cause the corks to fly, like sparks, upward. 1839 Salem Gaz. 12 Apr. 2/3 The house was O.K. at the last concert, and did credit to the musical taste of the young ladies and gents. 1839 Evening Tattler (N.Y.) 2 Sept. 2/2 These ‘wise men from the East’‥are right‥to play at bowls with us as long as we are willing to set ourselves up, like skittles, to be knocked down for their amusement and emolument. OK! all correct! 1839 Boston Even. Transcript 11 Oct. 2/3 Our Bank Directors have not thought it worth their while to call a meeting, even for consultation, on the subject. It is O.K. (all correct) in this quarter. 1839 Philadelphia Gaz. 12 Nov. 2/1 Yes—that's good—O.K.—I.S.B.D. [sc. it shall be done]. 1840 Morning Herald (N.Y.) 30 Mar. 2/1 A few years ago, some person accused Amos Kendall to General Jackson of being no better than he should be. ‘Let me examine the papers,’ said the old hero.‥ The General did so and found every thing right. ‘Tie up them papers,’ said the General.‥ ‘Mark on them, “O.K.”,’ continued the General. O.K. was marked upon them. ‘By the eternal’, said the good old General‥, ‘Amos is Ole Kurrek (all correct) and no mistake.’ Ibid. 21 Apr. 2/4 The Brigadier‥reviewed his Brigade‥and pronounced every thing O.K. 1840 Boston (Mass.) Daily Times 15 Dec. 2/3 What is't that ails the people, Joe? They're in a kurious way, For every where I chance to go, There's nothing but O.K. 1847 Robb Squatter Life 72 (Farmer) His express reported himself,‥assured Allen that all was O.K., and received his dollar. 1852 Judson Mysteries of N. York iv. (ibid.), 'Tis one of us; it's O.K. 1853 F. Townsend Fun & Earnest 14 To the earnest inquiries of another, he simply respondeth, O.K. 1864 Boy's Own Mag. Nov. 450/1 No thought of taking the trouble to find out whether the order was O.K., or ‘orl korrect’, as Sir William Curtis phrased it. 1865 W. H. Russell Atlantic Telegraph 61 The communication with shore continued to improve, and was, in the language of telegraphers, O.K. 1866 N. & Q. 18 Aug. 128/2 The following telegram has been received from Mr. R. A. Glass‥‘O.K.’, (all correct). 1874 E. S. Ward Trotty's Wedding Tour xiii. 133 We had an O.K. time till we went to bed. 1886 Lantern (New Orleans) 29 Sept. 3/2 Favetto umpired the game all O.K. 1888 Troy Daily Times 20 Feb. (ibid.), The Canadian customs-house is required to stamp an American vessel's paper O.K. 1894 C. H. W. Donovan With Wilson in Matabeleland xi. 253 As our American friends would say, we were still ‘O.K.’ 1898 Daily News 21 Jan. 7/1 In one of his letters from America defendant said‥he was ‘All O.K.’.‥ Mr. Justice Ridley—It means ‘all correct’, I understand. 1900 Law Times 10 Nov. 35/2 The State Court [U.S.] seems to have decided that when a lawyer marks such a decree O.K., he is, by so doing, estopped from questioning that decree by appeal. 1918 [see wet a. 4b]. 1922 D. H. Lawrence England, my England 101 At first Joe thought the job O.K. 1922 J. Reith Diary 14 Dec. (1975) ii. 128 He said‥that if things went OK I should get a rise soon. 1932 H. Nicolson Public Faces i. 8 ‘O.K.,’ he had said, ‘I'll remind old Peabottle.’‥ The expression ‘O.K.’ was not one which should be used in the Foreign Office, and least of all by an Assistant Private Secretary. 1937 D. L. Sayers Busman's Honeymoon viii. 148 ‘I Say, Mr. Superintendent, are you going to want me any more? I've got to get back to Town.’ ‘That's O.K. We've got your address.’ 1939 Times 24 Oct. 4/5 ‘O.K.’ is an abbreviation of the expression ‘Orl korrec’—all correct. It is English, I think Cockney—not an Americanism. I was born in the sixties and remember it when I was a boy. 1940 ‘N. Blake’ Malice in Wonderland i. ii. 20 Anything that was efficiently organised was O.K. by Paul Perry. 1941 Coast to Coast 1941 224 He'd have reckoned it was O.K. to have gone or to have done what I did. 1957 J. Montgomery Twenties xviii. 262 By mid-1929, when sound films had spread across Britain, there was hardly a town or village without some child who was saying ‘O.K.’ when previously he would have said ‘Yes’. 1968 Encounter Sept. 22/1 Direct transliterations from Yiddish or ‘Yinglish’ versions thereof.‥ O.K. by me. 1973 Railway World Apr. 172/2 It seems OK now to refer to that bit of the Mae Khlaung as the ‘River Kwai’. 1973 [see the verb, below]. 1976 Publishers Weekly 12 Jan. 52/2 The older dog asks if Pepper will allow him to go along for awhile and Pepper says ok. 1976 Punch 11 Feb. (recto front cover), Harold rules—OK? 1976 Spectator 15 May 3/1 George Davis was released by the Home Secretary, to the delight of headline writers, and the groans of others. The Spectator is bored by that line OK? 1976 Sunday Times 16 May 42 When George Davis stepped out of Parkhurst prison last week few headline writers could resist the temptation. George Davis is free OK? (the Sun), George Davis is freebut is it OK? (the Guardian). 1976 Observer 13 June 1/5 He added belligerently: ‘I don't want to answer no more questions, OK? No disrespect to the court.’ 1976 Sunday Express 4 July 6/3 He kept going on and on: ‘‥there are certain standards to be maintained in first-class compartments.’‥ And when he left the train‥he gave‥a look which said: ‘First Class Rules—O.K.?’ 1977 Times 26 Apr. 8/4 The popular graffiti— Rules-OK, which originated amongst the Glasgow razor gangs of the thirties. 1977 Zigzag June 31/1 We could have had a great album, rather than an OK album.

b. Used as a slogan by the Democrats in the American election campaign of 1840, influenced by the initials of Old Kinderhook, a nickname for Martin Van Buren (1782–1862), the Democratic candidate for the presidency, who was born at Kinderhook in New York State. O.K. Club, a Democratic club of New York City in 1840. Obs. exc. Hist.

1840 Democratic Republ. New Era 23 Mar. 3/2 (Advt.), The Democratic O.K. Club are hereby ordered to meet at the House of Jacob Colvin. 1840 Newark Daily Advertiser 28 Mar. 2/4 The war cry of the locofocos was O.K., the two letters paraded at the head of an inflammatory article in the New Era of the morning. ‘Down with the whigs, boys, O.K.’ was the shout of these poor, deluded men. 1840 National Intelligencer (Washington) 7 Apr. 1/2 Already the Locofocos have got out their banners and procession, and ‘the Butt-enders’ and ‘Point-enders’ are marching at night through our streets, led by the so-called ‘O.K.’ club, which is just now a cant phrase in Tammany. 1840 Democratic Republ. New Era 27 May 2/6 We acknowledge the receipt of a very pretty gold Pin,‥having upon it the (to the ‘Whigs’) very frightful letters O.K., significant of the birth-place of Martin Van Buren, old Kinderhook, as also the rallying word of the Democracy of the late election, ‘all correct’.‥ Those who wear them should bear in mind that it will require their most strenuous exertions‥to make all things O.K. 1948 Partridge World of Words (ed. 3) 175 O.K. was in 1840 the watchword of the O.K. Club, that Democratic Club of New York City which took its name from Old Kinderhook, nickname of Martin van Buren (1782–1862), born at Kinderhook in New York State and in 1836–40 the President of the United States.

c. Socially or culturally acceptable; correct; fashionable, modish; having or showing prestige, high-class.

1869 Henry De Marson's New Singer's Jrnl. xxxv. 246 The Stilton, sir, the cheese, the O.K. thing to do, On Sunday afternoon, is to toddle in the Zoo. 1899 R. Whiteing No. 5 John St. xxiii. 233 She objected to the parting of the ass's mane as ‘too O.K. for a moke’. 1950 S. Potter Some Notes Lifemanship i. 30 The word ‘diathesis’‥is now on the O.K. list for conversationmen. Ibid. v. 78 Just as there are O.K.-words in conversationship, so there are O.K.-people to mention in Newstatesmanship. 1957 Observer 22 Sept. 5/4 She left her campaign to save the theatre in the elegant hands of the Piccadilly and St. James's Association Ltd.—a very O.K. organisation of local shopkeepers and business, who like to keep the district nice. 1958 Spectator 19 Sept. 360/3 Mr. Macmillan ended his letter by saying we must treat this crisis ‘calmly and constructively’. Both these are very OK words just now. 1960 New Left Rev. May–June 55/1 To give up his clerk's post in favour of a much better paid (but socially less OK) job in a factory. 1963 Listener 17 Jan. 140/3 In an eminently ‘Third Programme’ talk‥he drew a comparison between this opera and his recent King Priam which was bedevilled by O.K. names and words. 1973 Times Lit. Suppl. 8 June 650/5 Handy quotations from such OK literary luminaries as Macaulay, Nietzsche, Strindberg, [etc.].

B. n. a. A member of the O.K. Club (see A. b, above). Obs.

1840 Morning Herald (N.Y.) 30 Mar. 2/1 The O.K.'s are now the most original and learned locofoco club of the day. Ibid. 4 Apr. 2/1 All the clubs of Buttenders, O.K.'s, N.C.'s, [etc.]. 1840 Boston Even. Transcript 15 Apr. 2/1 The tail of the Democratic party, the roarers, buttenders, ringtails, O.K.'s (flat burglary this latter title) and indomitables.

b. The letters ‘O.K.’, esp. as written on a document or the like, to express approval of its contents; an endorsement, approval, or authorization.

1841 ‘Dow, Jr.’ Short Patent Sermons 106 Fortitude‥ infuses new life into his soul, while Hope adds an O.K. to his condition. 1896 Congress. Rec. 5 Mar. 2507/1 The deputy marshall‥would send word to the prosecuting attorney asking for an ‘O.K.’ 1901 Merwin & Webster CalumetK’ xiv. 273 A formal permit‥signed by Porter himself, and bearing the O.K. of the general manager. 1910 S. E. White in Sunset Sept. 311/1 The high official added his OK to the others. 1925 H. Crane Let. 21 Oct. (1965) 218 My questionnaire‥had won an OK sign in the upper right corner. 1930 Liberty 11 Oct. 30/3 Rube copped a sneak on the joint to find out if it was ready. In twenty minutes he gives us the O.K. 1956 Rev. Eng. Stud. VII. 440 It is Pound who is to give the O.K. to the gods (not to God). 1961 L. Mumford City in Hist. xvii. 535 The fifth vice-president whose name or O.K. sets the final seal of responsibility upon an action.

C. v. trans. To endorse by marking with the letters ‘O.K.’; to approve, agree to, sanction, pass.

1888 Missouri Republican 25 Jan. 10/4 The expression, ‘Please O.K. and hurry return of my account,’ is grammatically correct. The noun account is governed by the preposition of, and is also the object of the active transitive verb O.K. 1891 Congress. Rec. 13 Feb. 2635/2 If those who were to go into the clerical service of the Government were to be ‘O.K.'d’ by any one except the Civil Service Commission. 1898 H. E. Hamblen Gen. Manager's Story 82 He hunted the hook over until he found the 227's report signed, Grinnell, O.K'd., and signed by the man who had done the work. 1921 R. S. Woodworth Psychol. xix. 505 Not that Freud would OK our account of dreams up to this point. Far from it. 1923 Galsworthy Captures 192 He finished pencilling, O.K.'d the sheets,‥and went back to his room. 1932 E. Wilson Devil take Hindmost xxi. 224 The company submits plans to us and we O.K. them.‥ We've O.K.'d Boulder City. 1942 E. Paul Narrow St. xxvii. 238 Of course, he [sc. Petain] had not counted on having the decrees he signed dictated by a German Führer, or at least O.K.'d when their hearts beat exactly as one. 1973 P. Dickinson Gift v. 76 ‘OK, OK,’ said Mr Venn soothingly.‥ But you know quite well head office wouldn't OK it.‥ I'm not going to risk it.’ ‘OK,’ said Mr Palozzi. 1976 Columbus (Montana) News 27 May 3/4 Smith's report‥was not officially OKed by the War Department for release until July 9.