The outgoing man has been at the north London club for 44 years and has been a loyal deputy to Arsene Wenger during his time in England.
The French coach was full of praise for Rice as he bows out of the game, and thanked the Gunners legend for his considerable efforts.
“He’s just been tremendous. It’s a sad, sad, sad day,” he told reporters, published in The Telegraph.
“His life was linked with Arsenal and Arsenal have been privileged to have him as a player, a captain, a coach, and personally I’m very grateful for his contribution to my period here.’’
Bould has been promoted from his role as youth-team coach, and Wenger is glad to have a familiar face filling the role.
“His qualities are that he has experience of the top-level game, he has managed here, he knows our football philosophy so there’ll be continuity,” he admitted.
Arsenal finish their Premier League campaign away to West Brom on Sunday, and must get all three points if they are seal third place.
By Gareth McKnight