Cribbs, who worked out for the Colts last week, was with the Browns from 2005 to '12, where he returned 11 kicks -- eight kickoff and three punts -- for touchdowns during his time there. He played six games with the New York Jets last season after being released by the Oakland Raiders.
Signing Cribbs adds depth to the receiver position and could signal the end of Griff Whalen returning punts and kicks, but the Colts still need help at running back. With Bradshaw out, the Colts are left with Trent Richardson and Daniel "Boom" Herron as the only two active backs on the roster.
"Between Trent and Boom and whoever, whatever happens from a roster mechanics standpoint, that's who will be back there," Colts coach Chuck Pagano said Monday.
The Colts also signed tight end Weslye Saunders to the active roster and waived linebacker Victor Butler on Tuesday.
The team has also begun researching running back Ben Tate -- including his character and potential fit in Indy's scheme -- and appear interested in possibly claiming him off waivers from the Browns, a source told ESPN.com's Jeremy Fowler.
ESPN's John Clayton contributed to this report.