Shipley, 26, is expected to compete with Gino Gradkowski for the starting center job with the Ravens.
The trade will be finalized after Shipley passes a physical.
Shipley told The Baltimore Sun that he was "fired up" by the trade.
"It's a great opportunity for me. I thought I played well enough as a starter to earn a little respect around the league and get a little buzz. The Ravens get a hard worker with me. I had to work for everything I got my whole life," he told the newspaper.
Matt Birk retired this offseason after starting every game at center for the Ravens the past four seasons.
After the Pittsburgh Steelers selected Shipley in the seventh round of the 2009 draft, he was on the practice squad for the Philadelphia Eagles for two seasons before making the active roster for the Colts. Shipley started five games last season for Indianapolis.
He played a key role on a Colts offensive line that was often decimated by injuries. He participated on special teams for Indianapolis in an AFC wild-card game in Baltimore last season.
But Shipley became expendable after the Colts selected Khaled Holmes, a center and guard from Southern California, in the fourth round of last month's draft -- part of Indy's revamped offense line that has added four new players through free agency and the draft.
Information from The Associated Press was used in this report.