The Dutchman completed his big-money move to Manchester United on Friday, penning a four-year deal with the 12-time Premier League champions.
Reports had suggested that Wenger will turn to Jack Wilshere to succeed Van Persie to lead the Gunners, but he has named the Belgium international instead.
Vermaelen has struggled with injuries since his move to Emirates Stadium from Ajax in 2009, but Wenger is confident that the defender can step up to the plate.
Ahead of Arsenal's Premier League opener against Sunderland, Wenger announced his new captain and vice-captain, saying: "It is [Thomas] Vermaelen and [Mikel] 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."
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