After eight years in north London, the Dutch striker took the controversial call to link up with a Premier League rival in the summer of 2012.
He had been a prolific presence with the Gunners, netting 132 goals in 278 appearances.
Van Persie had just one FA Cup success to show for those efforts, though, and made the decision to join United in a bid to secure more major silverware.
He became a Premier League title winner in his debut campaign with the Red Devils and insists he would not do anything differently if given the chance to turn back the clock.
"I was the captain, top scorer and we came third that year. But just sometimes you feel you need a challenge, a new adventure.
"If I hurt people, I'm sorry. But that's me. I made that decision and I stand by it. But that doesn't mean that I look in a negative way towards Arsenal.
"I cannot say one bad word about Arsenal Football Club - it is a beautiful football club, I had a fantastic time there. I arrived as a little boy, I left as an adult, as a mature player.
"I don't have a bad feeling towards anyone at Arsenal, I'm thankful towards them, for the chance they've given me, for the mistakes I made over the years - because I took a few silly red cards but Arsene still put me on - and just the whole family feeling of the club.
"During that whole process of leaving, Arsene Wenger and I never had an argument or a big fight, we just sometimes on certain levels had different ideas.
"At the crucial moments, you have to make tough decisions, and it was a very tough decision. But you have to stand behind them and this is what I did.
"I know if you make decisions like that, you're not going to please everyone. I learned quite a while ago that I will just be myself, I will make decisions about my life and I will accept them."
Van Persie, who also won a second Premier League Golden Boot while with United, admits he needed silverware in Manchester to justify his transfer and prove a point to those who questioned him.
He added: "Thank God I won the league there!.
"That was the target. In that first year, everything coming together was really special.
"I got half the [goalscoring] chances at Manchester United than the year before at Arsenal, and I scored almost the same amount of goals. So then you just know that it goes your way.
"I got help from my colleagues, from Sir Alex - he really pushed the guys to pass the ball to me. After a few months, everyone at the club had a feeling like, 'OK, this is going to be our year'. Difficult games, we won. Lucky goals were going in. When you know it's going your way..."