The 35-year-old, who made more than 600 club appearances during his career after starting out at Cannes in 1993, joined Manchester City in January 2010, featuring 45 times for the Blues in all competitions.
Vieira is to remain at Eastlands, becoming the club's new Football Development Executive.
And Gunners boss Wenger has hailed the combative midfielder, who made in excess of 400 appearances for the club after arriving from AC Milan for £3.5 million in 1996.
Vieira guided Arsenal to three Premier League and four FA Cup titles during his nine-year stay in North London, captaining the club during their famous 2003/04 Premier League triumph, in which the Gunners went the entire 38-game campaign undefeated.
"You can only have lot of respect for what Patrick has achieved," Wenger told the club's official website. "His career is sensational. He was an exceptional player for us.
"We have classy players in midfield now but Patrick was special. He was a tall player with good technique.
"You do not compare [old players with new players]. We have exceptional players in midfield with their own character. But at Arsenal we will be forever grateful for Patrick’s contribution."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.