English publication 'The Daily Mail' reports that the Brazilian will undergo his medical on Tuesday evening before being unveiled as a 'Blues' player.
Chelsea have reportedly agreed to pay an initial fee of £17.5m for the 23-year-old, with a further £5.2m coming in the form of add-ons.
Antonio Conte's side had originally plotted a double swoop for both Palmieri and Roma team-mate Edin Dzeko, but the move for the latter collapsed due to what Chelsea saw as "excessive" wage demands.
Palmieri has yet play for the 'Seleçao' internationally, but his arrival will provide Conte with comeptition for Marcos Alonso following Baba Rahman and Kenedy's loan moves to Schalke and Newcastle United respectively.