A league source said Wednesday it was a one-year deal.
For the Browns, it's a one-year flier as the team seeks players to compete for the free safety spot vacated by Tashaun Gipson, who signed with the Jaguars.
"It's a blessing. It feels like being drafted all over again," Moore said in the Browns statement. "I can definitely sense the aura on how this program is trying to change things around. Before I set foot in the premises, I've known the great history of the Cleveland Browns, from former UCLA great Eric Turner to Don Rogers to Thom Darden, it's a great place to be and I really felt like this was a great opportunity for me and a great fit, so I'm really excited."
Moore was released by the Houston Texans on March 3 after signing a three-year, $12 million deal with the team last March. He became Houston's starting safety but did not have a good year and was benched after Week 7. Not only did the Texans take him out of the starting lineup, they made him inactive for the rest of the season.
His release saved the Texans about $2 million in cap space.
Moore spent the first four years of his career with the Denver Broncos, starting at least seven games per season and 48 games in all. He will perhaps be most remembered during his time with the Broncos as the defensive back closest to Jacoby Jones on a game-tying play in what became a crushing double-overtime loss to the Baltimore Ravens in a divisional playoff game in the 2012 season.