1891: The earliest attestation of 'populist' in OED, from The New York Times, is dated 12 Jan 1891. The attestation is for sense A.1, "An adherent of a political party formed in the United States in 1892 to represent the interests of the entire population. Now hist.":
It later transpired that arrangements had been made by the Populists' majority in the Senate with Populist members in the House.
As pointed out in a comment (by DavePhD), however, the quote is misdated in OED (as is their 1891 quote attesting the adjective). The first use of 'populist' in what OED gives as sense A.1 appears in a newspaper almost six months later (The Progressive Farmer, Winston, North Carolina, 2 Jun 1891; see answer given by DavePhD).
1895: The derivation of OED sense A.2 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 (Irish English), renders moot the question of whether the primary historical sense is "after" Russian narodnik:
Derry Journal, 31 October 1849 (paywalled link).
While the attestation in the 1849 Londonderry Journal could be "after" the Russian, I found no evidence supporting that origin. The attestation also contradicts that the historically primary (first) sense is from US use denoting a specific political party, as per the evidence presented for the earliest sense given by OED, sense A.1.
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'.
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) 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 sense of 'most popular' to the agent noun 'one who makes popular.
Raleigh Times, North Carolina, 20 Apr 1849, paywalled.
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:
Wexford Constitution, 25 May 1859 (paywalled).
South London Press, 12 November 1881 (paywalled).
Manhattan Nationalist (Manhattan, Kansas), 29 Dec 1881 (paywalled).
Reynolds's Newspaper (London), 03 February 1889 (paywalled).
Thus, aside from the readily apparent eytmological borrowing of 'populist' from the 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.