Welbeck has not played since sustaining a broken ankle during a Europa League match in November.
Welbeck’s exit broke after he was honoured in front of the Emirates Stadium crowd alongside Juventus-bound Aaron Ramsey and retiring Petr Cech following the 1-1 draw with Brighton on Sunday.
“I spoke with the club about this situation. The decision is he’s going to leave,” Emery said at the end of his press conference on Sunday.
Welbeck joined Arsenal from United in 2014 and won the FA Cup with the north London side, where he was often utilised as an attacking option off the bench.