Van Persie only took the armband last summer following the sale of Cesc Fabregas to Barcelona but will sign for United later on Friday in a deal worth a reported £24 million.
Arsene Wenger confirmed in his morning press conference that Vermaelen will captain Arsenal for the coming season.
Midfielder Mikel Arteta has also been named as the club's vice-captain.
Wenger said: "The new captain is Vermaelen and [the vice-captain is] Arteta.
"Vermaelen was vice-captain, so it is a quick decision. I think we have many potential captains in the squad, but at the moment it will be like that."
Vermaelen joined Arsenal in a £10m deal from Ajax in July 2009 and has made 67 Premier League appearances for the Gunners.
He has formed an effective partnership with Frenchman Laurent Koscielny at the heart of the Arsenal defence and has also contributed 13 goals in the Premier League.
Van Persie will become the fifth captain that Arsenal have sold in the past seven years when he completes his move to United.