Hartley was let go Monday as Cleveland also signed defensive back Charles Gaines, the club's sixth-round pick, and signed eight players who participated in this past weekend's rookie minicamp.
Hartley played in Cleveland's final two games last season and made all three field-goal attempts. He kicked in 57 games for New Orleans from 2008-13 and also kicked for St. Louis.
Cundiff received an injury settlement last season after hurting his knee in practice. He missed five kicks in a five-game stretch before getting hurt.
The Browns are expected to sign another veteran kicker. Special teams coordinator Chris Tabor said over the weekend ''that position is wide open.''
Gaines is the third of Cleveland's 12 draft picks to sign.