The deal was concluded on Monday, two days after the Browns reached a breaking point with Gordon, who has been suspended for much of his NFL career.
Gordon played in Cleveland’s season opener, but reported to the team on Saturday with a hamstring injury after practising all week.
The Browns have been supportive of Gordon, but the team felt betrayed and decided it was time to cut ties.
Gordon’s talent had caused the Browns to hang onto him while he dealt with drug and alcohol dependence.
He missed training camp to receive treatment and his team were cautiously optimistic he would help them this season.
“There were things that we do not want to have happen here,” Browns head coach Hue Jackson said on Monday about the trade.
“We made a decision that is this is best for our football team moving forward.”
In New England, he will be reunited with former Cleveland and Baylor team-mate Corey Coleman, who had his own issues with the Browns before being traded last month.