The Dutch international, who has been with the Gunners since 2004, has often skippered the side on a temporary basis.
"Robin van Persie will be the captain this season," manager Arsene Wenger confirmed to the club's official website.
"He is a leader through the way he plays, through his attitude and through his desire to win.
"He's been at the club a long time and he's a technical leader as well. Thomas Vermaelen will assist him. It's the decision I have made and I'm confident the group will respond to it."
The 28-year-old will lead Arsenal out for the first time in his new role this Saturday when Liverpool visit the Emirates Stadium.
He is suspended for this evening's Champions League qualifier against Udinese.