The program is to premiere on the cable television network Aug. 16.
Elba will play Lenny, a painter who forms a relationship with the show's main character, played by Laura Linney, the network said.
The 13-episode series is currently shooting in Stamford, Conn.
Elba previously appeared on the U.S. shows "The Wire" and "The Office." He is currently starring as the lead in the U.K. series "Luther."