He began playing at three and his first composition was at six. He began his professional career in Rome in 1979 and later attended the Juilliard School. In 1984 Keyboard Magazine named him Best Pianist. In 1989 he left New York City, where he had settled, for Cologne. By that point he had been a member of Ray Anderson's and Perry Robinson's quartet. He has also won numerous piano competitions and did an album with Paul Motian. He also worked with tuba player Michel Godard or Eckard Koltermann Collage 11 with Barre Phillips, Theo Jörgensmann and Lauren Newton.
Nabatov made his name with a series of inventive trio albums with Mark Helias and Tom Rainey; he also often works with the trombonist Nils Wogram in duet or in larger ensembles. His most important work so far, however, has been a series of albums on Leo devoted to jazz tone-poem responses to Russian authors. Nature Morte is a setting of a poem by Joseph Brodsky; The Master and Margarita an all-instrumental response to the novel of the same name by Mikhail Bulgakov; and A Few Incidences contains octet settings of the enigmatic texts of the poet Daniil Kharms. Crucial to the two vocal discs have been the contributions of British singer Phil Minton.