Beasley, the No. 2 overall pick in the 2008 draft, averaged 7.9 points, 3.1 rebounds and 15.1 minutes while playing 55 games last season with the Miami Heat.
The Grizzlies announced the addition of the 25-year-old Beasley on Thursday.
The Grizzlies also announced they've added Patrick Christopher, Luke Hancock and Kalin Lucas, forward Earl Clark and center Hassan Whiteside to their training camp roster. Clark averaged 4.8 points, 2.6 rebounds and 14.2 minutes in 54 games with the Cleveland Cavaliers and New York Knicks last season.