Former Arsenal player Steve Bould will replace him, manager Arsene Wenger said.
Rice's last match as Wenger's No.2 will be the Premier League season finale at West Bromwich Albion on Sunday when Arsenal will attempt to seal third place in the table.
He played 528 times for Arsenal over 14 seasons and after a four year spell at Watford from 1980-84, returned to Arsenal to coach the juniors and became Wenger's right-hand man when the Frenchman joined the club in 1996.
Wenger described Rice as an "Arsenal legend".
"He has committed almost his whole life to Arsenal Football Club, which shows huge loyalty and devotion," Wenger said.
"Pat has been amazing for me over the past 16 years.
"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."
