The old English rivals meet at Old Trafford in the Premier League this weekend, with the Dutch international facing his former club for the very first time.
Van Persie signed a four-year deal with the Red Devils in August, after deciding against a contract extension to remain in north London, much to the disappointment of Arsene Wenger, and the Gunners fans.
And, to make matters worse, he's started the 2012/13 campaign in scintillating form, scoring seven goals in just nine league games for United, going into Saturday's clash.
"You have to be courageous to make the move and Robin took the decision," said Silvestre, who himself made 326 appearances for Manchester United and 38 for Arsenal. "He is enjoying his football, and has been scoring. He has had a great start at the club.
"He is not hiding on the pitch, is taking responsibility and always asking for the ball. Wayne Rooney was injured and he took the responsibility for the team by scoring the goals.
"Robin is under the same pressure as he was at Arsenal. He is a goalscorer, you expect him to put the ball in the back of the net and to have the same statistics as last year.
"If he stays fit, then there is the potential to form a great partnership with Wayne Rooney. Robin came to win trophies and Wayne is still thirsty for trophies. You couldn't ask for a better pairing."
Silvestre enjoyed nine successful seasons under Sir Alex Ferguson at Old Trafford, winning five Premier League titles, one FA Cup, one League Cup and a Champions League crown, before heading to Arsenal in 2008, where he became the first player to transfer directly between the two clubs since Viv Anderson in 1987.
Four years later, Van Persie moved in the opposite direction, to join Silvestre as the only other player to have worked under both Ferguson and Wenger in the Premier League.
"I think the Arsenal fans may boo Robin because he spent a lot of time there and the fans don't want to lose their best assets," the Frenchman continued, looking ahead to the weekend encounter.
"Losing him to one of the main rivals is not good and they have the right to be angry but that is football, you can't keep a player against their will, but he won't celebrate if he scores as he still has a lot of respect for the club like I do."