The Angels abruptly announced the move Monday before the first pitch of their game against Texas.
"This was an upside gamble that I deemed worth the risk, and unfortunately it did not transpire for either Ryan or the club," Angels general manager Jerry Dipoto said.
Los Angeles signed Madson to a one-year, $3.5 million deal in late November, hoping the former Philadelphia closer could fill the same role in Anaheim.
But Madson developed elbow soreness during spring training and never made it back to the big leagues with his hometown Angels despite rehabilitation assignments and extra work in Arizona.
"We signed Ryan with the belief that he would return to the mound this season and positively impact our team," Dipoto said. "It became increasingly more apparent to us that he was not going to pitch for the Angels this season. Our medical team has spent much time, effort and resources in the effort to facilitate a healthy return. It's been a long and difficult process for all involved."
Madson hasn't pitched in the big leagues since 2011, having had season-ending surgery in April 2012 after signing an $8 million deal with the Cincinnati Reds. Madson also never pitched for the Reds.