Terms of the deal weren't disclosed Wednesday.
Fleener was selected in the second round, 34th overall.
Teaming with fellow Colts rookie Andrew Luck at Stanford, Fleener had 34 catches for 667 yards -- a 19.6-yard average -- and 10 touchdowns last season. In 51 career games, he had 96 catches for 1,543 yards and 18 TDs.
He had his best game in Stanford's 2011 Orange Bowl victory over Virginia Tech, finishing with six receptions for 173 yards and three touchdowns.
The Colts open training camp on Saturday.