1789, "a singer;" see melody + -ist. Perhaps from or based on French mélodiste. By 1826 as "a composer of songs and melodies."
Entries linking to melodist
melody n.
c. 1300, melodie, "vocal or instrumental music, a succession of agreeable musical sounds," from Old French melodie "music, song, tune" (12c.) and directly from Late Latin melodia "a pleasant song" (in Medieval Latin also "music" generally), from Greek melōidia "a singing, a chanting; a choral song, a tune for lyric poetry," from melos "song, part of song; limb, member" (a word of uncertain origin) + ōidē "song, ode" (see ode). From late 14c. as "a song of clear and balanced form." Sense of "a series of tones so related to one another as to produce a distinct musical phrase or idea, a tune" is by c. 1600. Meaning "the principal voice-part in a harmonic composition" is by 1880.
-ist
word-forming element meaning "one who does or makes," also used to indicate adherence to a certain doctrine or custom, from French -iste and directly from Latin -ista (source also of Spanish, Portuguese, Italian -ista), from Greek agent-noun ending -istes, which is from -is-, ending of the stem of verbs in -izein, + agential suffix -tes.
Variant -ister (as in chorister, barrister) is from Old French -istre, on false analogy of ministre. Variant -ista is from Spanish, popularized in American English 1970s by names of Latin-American revolutionary movements.