He agreed to the deal over the weekend. The contract signed Tuesday includes a player option for 2015-16.
Deng is entering his 11th NBA season, after spending almost his entire career with the Chicago Bulls. He appeared in 40 games with the Cleveland Cavaliers following a trade last season. In Miami, he figures to compete for the starting spot vacated last week when LeBron James left the Heat for a return to the Cavaliers.
Deng has averaged 16.0 points in his career. He was picked No. 7 overall from Duke in the 2004 draft.