Griffin, the No. 2 overall pick in the 2012 draft by the Washington Redskins, was released before his fifth-year option hit the books at more than $15 million. Griffin was replaced as the starting quarterback in Washington before the 2015 season began by Kirk Cousins, who was retained in March with the Redskins' franchise tag.
"I'm excited about the opportunity to join the Dawg Pound and build something here in Cleveland," Griffin said. "I'm just excited to come in and compete. "Nothing's ever been given to me in my life. I just want to go out and compete with the guys and grow with this team."
The Browns cut ties with Johnny Manziel and their QB picture is still developing.
Josh McCown is under contract but would be 35 before the start of the 2016 season.
Cleveland also owns the No. 2 overall pick in the 2016 draft and sent a large presence, headlined by vice president Sashi Brown and head coach Hue Jackson, to the pro day workout of North Dakota State quarterback Carson Wentz in Fargo.
The Browns were also highly visible at Cal quarterback Jared Goff's workout last week.
Solving the quarterback pecking order remains a mission for a franchise that has failed to find a permanent solution at the position for nearly two decades. The next starter for the Browns would be the 25th since Cleveland's franchise was restored in 1999.