Roseman was born in Boston, and studied at the New England Conservatory of Music. Roseman toured Jamaica with The Skatalites and in Australia with the Christopher Hale Ensemble. He has also played with Steve Coleman, Dave Holland, Dave Douglas, Don Byron, John Zorn, Charlie Hunter, Mike Gordon, Soulive, Groove Collective, and Me'Shell Ndegeocello.
Roseman has led sessions for Enja Records as The Josh Roseman Unit. His sidemen include Peter Apfelbaum, Barney McAll, Ben Monder, Jonathan Maron, Billy Kilson, Ted Poor, Tony Barba, and Kirk Knuffke and special guests on the albums include Chris Potter, Liberty Ellman, Ben Perowsky, and Mark Feldman.