Bell was assigned to Triple-A Scranton, according to Newsday's Erik Boland.
The Yankees' bullpen is tied for 24th in the league with a 4.20 ERA entering Friday.
Bell was 1-1 with a 7.27 ERA in 13 appearances this season before he was released by the Rays on May 4. Tampa Bay acquired the 36-year-old from Arizona in a three-team trade in the offseason.
Bell made three straight All-Star appearances from 2009-11 for the Padres, leading the majors with 132 saves during that stretch. He is 38-32 with a 3.49 ERA in 11 big league seasons for the Mets, Padres, Marlins, Diamondbacks and Rays.
Yankees have signed @HeathBell21 to a minor league contract and assigned him to Triple-A Scranton. — Erik Boland (@eboland11) June 13, 2014