McCoy, who became expendable when Cleveland signed veteran free agent quarterback Jason Campbell last week, was traded Monday to the San Francisco 49ers for two draft picks.
The Browns confirmed the deal on the same day new coach Rob Chudzinski welcomed more than 60 players—including McCoy—for the start of the team's voluntary offseason conditioning program.
The Browns only said they received two "undisclosed" draft choices, but a person familiar with the deal told The Associated Press the team got a fifth- and seventh-round pick in this month's NFL draft in exchange for McCoy and Cleveland's sixth-round pick. The person provided details of the trade on condition of anonymity. The Browns now have seven picks in this year's draft.
McCoy is one of 18 quarterbacks to start for the Browns since 1999. The team's inability to find a franchise QB is among the biggest reasons Cleveland has made the playoffs just once in 14 seasons.
For a short period, McCoy showed promise of being the quarterback to revive the Browns. But he was flattened on a vicious hit in 2011, lost his job to Brandon Weeden last season and became the odd-man out after Campbell's arrival.
CBSSports.com was first to report McCoy's trade.
Last week, Browns CEO Joe Banner said the Browns would not release McCoy and would look for a trade partner.
A popular player with some Cleveland fans who felt he never got a fair shake, McCoy will also be reunited in San Francisco with former Browns kicker Phil Dawson, who recently signed a one-year free agent deal with the Niners.
Because of injuries to Jake Delhomme and Seneca Wallace, McCoy, who won 45 career games at Texas, was forced into the starting lineup as a rookie and made eight starts.
Though not blessed with a strong arm, McCoy's mobility in the pocket allowed him to make enough plays that the Browns kept him as their No. 1 QB in 2011. He started 13 games, but his season was essentially ended—and his career altered—when he took a helmet-to-helmet hit from Pittsburgh linebacker James Harrison.
The Browns allowed McCoy to return to the game despite having a concussion, and the team's mishandling of the situation led to the NFL making some changes to its policy on head injuries.
McCoy was in line to be Cleveland's starter in 2012, but the team chose Weeden in the first round. McCoy spent much of last season as the subject of trade rumors and he was knocked down the depth chart once Campbell was signed to a two-year deal.
Campbell is expected to play behind Weeden next season, but could challenge him for the starting job. The Browns also have quarterback Thaddeus Lewis, who made one start in 2012, under contract.
McCoy, who went 6-15 as a starter, appeared in three games last season. He came in after Weeden hurt his shoulder against Denver on Dec. 23, but McCoy sustained a right shoulder injury on one of the four sacks recorded against him by the Broncos and he was inactive for Cleveland's season finale.
McCoy completed 409 of 702 passes (53 percent) for 4,388 yards with 21 touchdowns and 20 interceptions with the Browns.