The Dutchman completed a switch to Old Trafford in the summer of 2012, with Arsenal reluctantly sanctioning a sale as Van Persie's contract entered its final year.
The Holland international has been an immediate success at United, with his prolific form firing the Red Devils to the top of the Premier League table.
Van Persie is delighted with how things have turned out, with the 29-year-old admitting that he needed to make a fresh start and take on a new challenge.
"Arsenal are a great club and I always had a good feeling but after eight years, sometimes you feel that you need a new challenge," Van Persie told Sky Sports in an exclusive interview.
"I found that challenge at Manchester United. I do feel that I am surrounded by champions.
"I do feel that this is exactly the right time to be here. I don't think it would have been better to come here earlier. Everything has gone this way for a reason.
"When I extended my deal a couple of years ago at Arsenal, I felt that was the right move for me - to stay and play because I wasn't finished there. Now, since last summer, I wanted to go for a big challenge, and this was the biggest challenge for me.
"I think every day tells me that I made the right move. It's nothing bad about Arsenal. No player is bigger than the club, Arsenal will always challenge for trophies and be up there. It was just that after eight years I was ready to move on and try something else."
On how things have gone for him at Old Trafford, Van Persie added: "On and off the pitch, everyone has been helpful. I have settled in well.
"The main thing is that from day one everyone gave me the feeling that I was welcome and that they were happy for me to be here. I was happy to be here, it was a new challenge for me and I was ready for that challenge. I am having fun.
"I am seeing things again which I haven't seen for a long time. When I first went to Arsenal years ago I saw things from (Dennis) Bergkamp and (Thierry) Henry that I had never seen in my life before. Now I am seeing those things again and that makes me happy.
"It's like being a kid in a sweet shop. This is having fun, enjoying myself. That's what I am doing, I'm just having fun."
Van Persie certainly is having fun, with 22 goals plundered in 28 outings - 18 of them coming in the Premier League.
He hopes there will be many more to come, with the injury troubles which plagued him in the past having been put firmly to one side.
He said: "If you go back to my injuries, people just look at stats and for a couple of years those stats weren't great. But most of those injuries were impact injuries, they can happen. It was mostly unlucky.
"I don't think it was me to blame, or the club medical staff to blame. I was just unlucky."