"It feels like being drafted all over again," Moore said in a statement released by the team.
He even honored the Browns' past by bringing up former safeties Eric Turner, Don Rogers and Thom Darden. Nice touch.
However, Moore comes with baggage.
He was the safety who was beat on the Baltimore Ravens' "Mile High Miracle" play in a playoff game in Denver in January 2013. On the play, Moore took a bad angle and allowed Jacoby Jones to get behind him in the final minute. Joe Flacco's 70-yard touchdown pass with 31 seconds left tied a game the Broncos should have won.
The Ravens won in overtime, and that play catapulted them to a championship.
Last season Moore started the first seven games in Houston, but after missing three tackles on touchdown runs in a loss to Miami he was benched and did not start the final nine games.
Whether it was coincidence or cause and effect, the Texans won seven of those nine games.
The two free agents the Browns have signed -- Moore and linebacker Demario Davis -- have something in common. Both had their playing time cut during the second half of last season.
Moore was benched for the final nine games, while Davis shared time in the final six.
The Browns needed safety depth after the departure of Tashaun Gipson, and Moore is a lower-priced alternative. At 26 he's actually a year older than Gipson.
The Texans thought enough of Moore to sign him as a free agent before last season.
Moore is looking at this chance the right way, as an opportunity to re-establish himself.