Four days after drafting Johnny Manziel, the Browns released the 30-year-old Young.
Browns owner Jimmy Haslam announced the move with Young on Monday during a speech at a Pro Football Hall of Fame luncheon.
Young, who didn't play in the NFL last season after being cut by the Green Bay Packers in the preseason, participated in the Browns' three-day minicamp before signing with the team May 1. The team signed veteran quarterback Tyler Thigpen on the same day.
In addition to Manziel and Thigpen, the Browns also have incumbent Brian Hoyer, who is recovering from knee surgery. Hoyer recently said he remains confident that he will be the club's starting quarterback this season.
Young spent five seasons with Tennessee. He started three games for the Eagles in 2011.
Former South Carolina quarterback Connor Shaw, an undrafted free agent, tweeted on Saturday that he is signing with the Browns, leaving with the Browns with four quarterbacks even after the release of Young and Tanney.
Information from The Associated Press was used in this report.