1891: The earliest attestation of 'populist' (noun and adjective) in OED is from The New York Times and is misdated 12 Jan 1891 (as observed by DavePhD — see comments). The attestation, which actually appears in The New York Times of the same day and month in 1893, is given for noun sense A.1:
An adherent of a political party formed in the United States in 1891 to represent the interests of the entire population. Now historical.
The same misdated attestation is abridged for the adjective, OED sense B:
Intended to appeal to or represent the interests of ordinary people; spec. of or relating to a political party formed in the United States in 1891 to represent the interests of the entire population (now historical).
The first use of 'populist' that I could find in OED sense A.1 appears 28 May 1891 (paywalled) in The American Nonconformist and Kansas Industrial Liberator (Winfield, Kansas; p 1, col 5). The article refers to the "Cincinnati Conference", an organizing convention held 19-21 May 1891:
"WE ARE WITH YOU."
(Copyrighted by the Reform Press Bureau.)
HE IS A "POPULIST."
There must be some short and easy way of designating a member of the third party [sc. decided at the Cincinnati Conference]. To say, "he is a member of the People's party" would take too much time. Henceforth a follower and affilliator of the People's party is a "Populist"; for a new party needs and deserves a new term.
This article, bylined "H.W. Ayer, Manager Reform Press Bureau" (op. cit., p 8 col 4), is likely to be the first print appearance of 'populist' in OED sense A.1; the text implies that Ayer originated that use of the term.
1895: The derivation of OED sense A.2, a "member of a Russian political party representing the peasantry and advocating agricultural collectivism", is said to be "after Russian narodnik". This sense is first attested by an author with a Russian surname, P. Milyoukov, in Athenæum of 6 Jul 1895:
The first [group] values primitive collectivism because it regards it as an inalienable trait in the character of the Russian people... [It] sticks to its old name of ‘Populists’.
1849, 1961: However, much earlier attestation of 'populist', from the 31 Oct 1849 issue of The Londonderry Journal, renders moot the question of whether the primary historical sense is "after" Russian narodnik:
On popular habits and character, too, I thought it [sc. "the famine"] had left an altering impress. The peasantry had one and all an altered and careworn look, as if taking thought for to-morrow had at last found and clung to them. In the villages there was small appearance of the fun and frolic so long characteristic of Irish populists.
Londonderry (now Derry) Journal, 31 October 1849 (paywalled link).
The racist and revisionist perspective expressed in this article should not be left unremarked. The "altered and careworn look" mentioned was no doubt caused by the extraordinarily severe circumstances imposed upon the Irish people by British misrule, not by any failure of the former to take "thought for tomorrow". Ireland was a net exporter of food during the so-called 'famine', which would be more aptly called a 'starvation' because it was a genocidal act of warlike repression upon one category of people by another.
While the use in the 1849 Londonderry Journal could, perhaps, be "after" Russian narodnik, I found no evidence supporting that origin. The early use also contradicts that the OED sense A.1, attested from US use denoting a specific political party, is chronologically the first use of 'populist'.
A careful examination of the context of the Londonderry Journal use, as shown in the clipping and surrounding material, suggests, rather, that the first sense of 'populist' in English was similar in many ways to OED sense A.4 (first attested from 1961):
A person who seeks to represent or appeal to the interests of ordinary people.
My tentative conclusion (pending corroborating or contradicting evidence) is that 'populist' in the clipping from The Londonderry Journal is used in the general sense of
A person who represents and participates in the interests of ordinary people.
The sense intended may, however, be nothing more nor less than "one who populates" (Ireland, in this case).
1890 and earlier; source of 'populist' in 'popularist'**: OED gives 'popularist' as a precursor of 'populist' in various senses, notably attesting it from The Times (London) of 12 Jan 1882 in a political sense resembling that of 'populist' sense A.1 (see above), but designating a German rather than a US political party, that is,
Saving, however, the Social Democrats and the Popularists, with a brace or so of aspiring Danes, the House could not be brought to see present reason in the motion.
Other senses of 'popularist' than that found in the earliest attestation provided by OED (1882) range in meaning from the jocular superlative "most popular" to the agent noun "one who makes popular".
At last some of the gals got so curious, they asked him whar he did cum from, any how, and as soon as he sed Indian-ee, Dick Mason becum one of the popularist young men in the settle-ment among the wimmen, jest 'cause he war from the same State.
Raleigh Times, North Carolina, 20 Apr 1849, paywalled.
Professor Tyndall insists on the necessity of imagination for the true scientist. Without it he cannot become more than a calculating mechanism. With it he can soar into realms from which ordinary mortals are excluded. To the popularist of science this same gift of a vivid imagination is not less important…
Manchester Courier and Lancashire General Advertiser, 15 September 1888, paywalled.
Most significant, though, in tracing the origins and development of 'Populist' in OED sense A.1, are multiple uses of 'Popularist' in both the US and British press to denote political parties. These uses are attested from 1859 to 1889, that is, from the years leading up to the adoption of 'Populist' in the specific sense given as OED's A.1, by the US press and, soon after, its adoption by the British press.
Examples of 'popularist' use from the British and US press, 1859-1889:
The word "Americanist" would suit many of them; but the mass of the Liberals would still, we hope, have too much British feeling to accept the name, although we do not forget that the blue and buff uniform of the Whigs was originally a fashion at the other side of the Atantic, and was sometimes worn beneath the Red Cap of the French Republic. The word "Popularist" would be eagerly accepted by the Liberals, but we could not allow it them, for many Conservatives are "Popularists"; besides, in the warfare of party our antagonists would be sure to cry us down as "un" or "anti" popularists. The phrase "Greatest Numberist" is, we admit, as barbarous as if Bentham minted it in one of his "ante-jentacular or post-prandial vibrations," justly satirized by Tom Moore; but there is a large class of floating "Liberals" whose creed might be embodied in the words, vox populi vox Dei. If the "greatest number" were for the Pope, they would be Papists; and if the amjority were anti-Christian, they would vote against Revelation. Let these men dub themselves; to us they are nondescripts.
Wexford Constitution, 25 May 1859 (paywalled).
The German Parliament is the most singularly constituted legislative body in Europe. At the present moment it is subdivided into no fewer than seventeen distinct political sections, without counting the "Savages," who pride themselves upon the speciality that they disagree with all the other denominations, and that every man's hand is against them. These seventeen "parties" rejoice in the following designations: Conservatives, Free Conservatives, German Conservatives, German Imperialists, National Liberals, Liberals, Secessionists, Progressists, Popularists, Poles, Clericals, Social Democrats, Christian Socialists, Particularists, Protesters, Autonomists, and Danes.
South London Press, 12 November 1881 (paywalled).
There are seventeen fractions of parties in the German Parliament, viz.: Conservatives, Free Conservatives, German Conservatives, German Imperialists, National Liberals, Liberals, Secessionists, Progressists, Popularists, Poles, Clericals, Social Democrats, Christian Socialists, Particularists, Protesters, Autonomists, and Danes.
Manhattan Nationalist (Manhattan, Kansas), 29 Dec 1881 (paywalled).
At the final division on the measure the Opposition was formed by the Liberalists — all but two — the Social-Democrats, the Poles, and a Popularist.
Reynolds's Newspaper (London), 03 February 1889 (paywalled).
Thus, aside from the readily apparent derivation of 'populist' from Latin populus plus the English suffix -ist, the use and development of 'populist' in all its senses involves the somewhat parallel use and development of 'popularist'. This is true not only of 'Populist' in the narrow US sense from 1891, but also of 'populist' in its earlier development from a general sense (1849) and its later devolvement back to a general sense of "one who advocates, represents, and participates in the interests and concerns of ordinary people", a sense which is firmly re-established by 1961.
Historical trends redefining 'populist': By 1896, the Populist Party was split between 'fusionists', who advocated merging with mainline Democrats, and who ultimately prevailed, and independents. However, for decades afterward (1900-1960), the predominant reference of the term was to the former US political party.
A sprinkling of uses of 'populist' ('populistic', etc.) in the more general sense of "representing ordinary people" does appear in the material I examined from approximately 1900-1960. The historical trends prompting the return of the general sense appear to have their origins primarily, if not exclusively, in the US, and particularly in the gradual absorption of the Populist Party into the Democratic Party mainline along with the successful marginalization of populism as a variety of socialism.