The Old Trafford giants confirmed on Wednesday evening that they had agreed terms with Arsenal - understood to be £24million - for the Dutchman.
Van Persie is now set to travel to undergo a medical and finalise personal terms with United.
Wenger insists he had no option but to sell van Persie because he had just a year left on his current deal and he had already refused to sign a new deal.
"He is at Manchester United, unfortunately for us. The transfer was finalised in the afternoon," said Wenger whilst working for French TV station TF1 on Wednesday.
"It's never great to lose players of that quality but he only had a year contract so we do not have a choice."
Wenger then stated that he had already signed Olivier Giroud and Lukas Podolski to cover for van Persie's departure.
"We have already recruited since we bought Giroud and Podolski who originally were intended to offset the departure of van Persie," he concluded.