The Browns traded Colt McCoy and a sixth round draft pick to San Francisco for the 49ers fifth and seventh round picks.
The picks the Browns receive are the 164th and 227th overall in this month's NFL Draft. The Browns sent the 173rd overall pick to the 49ers.
McCoy, who became expendable once the team signed Jason Campbell last week, will back-up Colin Kaepernick in San Francisco.
McCoy becomes the third quarterback on Monday to change addresses. The Seahawks dealt Matt Flynn to the Raiders, who dealt their quarterback Carson Palmer to Arizona.
McCoy started 21 games for the Browns in his three years in Cleveland, throwing for 4,388 yards for 21 touchdowns and 21 interceptions. He was 6-15 as a starter in those three seasons.
The former third round pick in 2010 will make $2.325 million in 2013.
McCoy joins former Browns kicker Phil Dawson in the Bay Area.
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