The Patriots selected O'Connell in the third round of the 2008 draft. He made appearances in only two regular season games with New England, lost the backup quarterback job to Brian Hoyer and had stints with multiple other teams.
O'Connell, 29, also worked with Johnny Manziel prior to the 2014 draft, in which he was selected in the first round. ESPN reported that the Browns didn't consider O'Connell's relationship with Manziel "a huge selling point."
In 13 starts for the Browns last season, Hoyer completed 55.3 percent of his passes for 3,326 yards with 12 touchdowns and 13 interceptions. In two starts last season, Manziel connected on 51.4 percent of his passes for 175 yards.
Hoyer is reportedly expected to leave the team in free agency.
Marvez also reported that Cleveland has hired Kurt Roper as a senior offensive assistant. Roper previously served as the offensive coordinator at Florida and Duke.