The Dutch striker attracted criticism when he swapped the Emirates Stadium for Old Trafford in the summer of 2012, but his countryman says it was right for all parties
Van Persie spent his first few years in north London as a talented but injury-prone winger before adapting his game to become the most feared striker in the Premier League.
The Dutchman's form attracted the attention of Sir Alex Ferguson and won his first league title following a £24 million move to Old Trafford in August 2012.
"I didn’t expect that he would be a striker, you know," Overmars, speaking to Absolute Radio's 'Rock 'N' Roll Football', said of Van Persie.
"I thought he would be a midfielder, but the boss, Wenger, was very good. At the time he bought excellent young players, and got Van Persie for £1.5m.
"When he came to Arsenal and got the chance to learn from Bergkamp, it was a great move for him. The transfer to Man United was not a big deal either. You have to give him credit.
"He played for Arsenal for eight years. He performed and delivered and then got a great transfer, so everybody should be happy."