The deal includes $3.8 million in guaranteed money.
The Browns selected Gordon last week in the second round of the NFL's supplemental draft. The team forfeited a second-round pick in 2013 to get Gordon, a talented and troubled player who was dismissed at Baylor after testing positive for marijuana after his sophomore season.
Browns general manager Tom Heckert said the team did exhaustive background checks on Gordon and are confident they're getting a player who can help them immediately.
Gordon had 42 catches for 714 yards and seven touchdowns in 2010 for Baylor. He transferred to Utah, but did not play in any games for the school.
Heckert said last week that the 6-foot-4, 224-pound Gordon has the potential to be a No. 1 wide receiver.
With Gordon signed, the only draft picks not under contract are running back Trent Richardson and quarterback Brandon Weeden. Last week, Heckert said he expected both to be signed by the time camp opens on July 28.
Also, kicker Phil Dawson will earn $3.8 million next season after previously signing the franchise tag. The sides had until Monday to work out a long-term deal.