Van Persie, 29, publicly declared his intent to leave the Gunners after another season without silverware, and with his contract set to expire next summer the club have opted to cash in on their prized asset.
The fee for Van Persie has not been discussed, but it is believed to be in the region of £24 million. Other clubs were interested – such as Manchester City and Juventus – but none willing to match Arsenal’s asking price.
Speaking to Eurosport's parent station TF1, Wenger complained that he would rather not have sold to one of his main rivals, but conceded that the likes of Paris Saint-Germain simply were not interested.
“To strengthen an enemy is the other negative point of this loss,” he said. “We wanted to avoid it but we couldn’t. Honestly, I’d rather sell him abroad, to Paris Saint-Germain for example.
“Manchester United know him and know his qualities. He’s really an exceptional player, believe me.”
Wenger also admitted his disappointment at losing a striker who scored 37 goals in all competitions last season, but insisted the club were well prepared for his departure.
He continued: “Van Persie is a great player so it’s always sad to lose such a player. But we must consider the economic reality and the will of the player.
“When you can’t succeed in extending the contract of a player that is in its last year, there is no other way but to let him go. It’s sad because he played for us for eight years. He’s 29 now. He was 21 when he came and it’s another bitter pill to swallow.
“A lot has happened before and we survived it all, but this is a real challenge because Van Persie scored 30 (Premier League) goals in a year, almost one per game. It’s a tough challenge for our new forwards to replace him.”
Wenger added that France striker Olivier Giroud had been signed as a direct replacement and, with Germany forward Lukas Podolski also joining the club, Van Persie’s exit will give them a chance to shine.
“The economic part of it is the only satisfaction. But money doesn’t go out on the field and play, players do," he said.
“It will give more chance to Giroud. When Van Persie is here, his name is the first on the team-sheet and the others follow. So there’s a void to fill.”
Van Persie is expected to sign a long-term contract at Old Trafford after passing a medical. Boss Sir Alex Ferguson said he was confident the deal would go through.
"The fee has been agreed, which we're delighted about," he said.
"He's on his way here from London to have a medical later. Hopefully, that goes according to plan.
"We hope he will be available for Monday night. It's great to have a player of the quality of Robin van Persie coming into the squad. I'm very pleased."