Rice's final match of his 44-year association with the Gunners will be Sunday's clash away to West Bromwich Albion, when the Londoners must match Tottenham Hotspur's result at home to Fulham in order to once again finish above their local rivals and secure an automatic spot in next season's Champions League.
Wenger told the club's official website: "Pat is a true Arsenal legend and has committed almost his whole life to Arsenal Football Club, which shows huge loyalty and devotion to this Club.
"Pat has been amazing for me over the past 16 years. When I first arrived at Arsenal, Pat was always there and taught me so much about this great club. I will always be indebted to him for his expert insight into Arsenal and football as a whole. On the training pitches and on matchdays, Pat has always been a passionate, loyal and insightful colleague, who we will all miss.
"Thank you Pat, we’ll miss you and all of us wish you and your family the best of health and happiness for the future. Although, we’ll still see Pat a lot, as I know he’s planning to come to all the home matches as a supporter."
At a press conference later on Thursday, Wenger confirmed that another former Arsenal defender and current youth team coach, Steve Bould, would take over the role.
Wenger said: "I always want to give a chance to people who know how we coach.
"Steve is a very good coach and brings a continuation of our philosophy."
Rice has served Arsenal with distinction since joining the club as a trainee and signing his first professional contract in 1966.
Over the next 14 years he made 528 appearances at right-back, winning a league and FA Cup double in 1971 and captaining the club to glory at Wembley again in 1979.
After finishing his playing career at Watford he returned to Arsenal as youth team coach, winning two FA Youth Cups.
In the interim period between Bruce Rioch's departure and Wenger's arrival as manager in 1996, Rice took charge of four matches, winning all three in the league.
At Wenger's side, Rice helped the first team claim three Premier League titles and four FA Cups, including two doubles in 1998 and 2002 and their famous unbeaten 'Invincibles' title-winning season of 2003/04.