Emirates Stadium manager Arsene Wenger has confirmed the 26-year-old centre-back will skipper the club and midfielder Mikel Arteta will serve as his deputy.
Vermaelen succeeds Van Persie as Arsenal's captain as the Dutchman is expected to complete a ?24million move to Manchester United.
There had been speculation Wenger could have turned to injury-plagued England international Jack Wilshere, but he has instead named Vermaelen.
The Belgium international has himself struggled with a variety of injuries since arriving at Arsenal in a ?10m move from Ajax in the summer of 2009.
But Wenger has faith in the centre-back, as he said at a press conference ahead of Saturday's Premier League season opener: "It is Vermaelen and 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."