In Disney's 1991 animated Beauty and the Beast, Alan Menken composed the music for the film’s songs.
Menken worked with lyricist Howard Ashman on the score, creating songs including “Belle,” “Be Our Guest,” “Gaston” and the title ballad. Their collaboration helped define the Broadway-influenced musical style of the Disney Renaissance.
Ashman died in 1991 before the film was released, and the completed movie was dedicated to him. Menken later continued working on Disney projects and composed the music for the 2017 live-action Beauty and the Beast as well.
The question is specifically about the composer, not the lyricist or the film’s voice cast. Menken wrote the melodies and musical arrangements, while Ashman supplied the words for the original songs in the animated film.