The former Spanish international, 34, joined City from Valencia in 2010 and has gone on to make 429 appearances and help them land 14 major trophies.
Begiristain said: "He's been unbelievable in football - especially here.
"He's spent 10 wonderful years, winning trophies and changing the dynamic of the club.
"He's been one of the leaders – with Vincent (Kompany), with Yaya (Toure) and Kun (Aguero). No one will forget what they've done.
"Not only the way David plays football but helping us be a successful club. He will always be remembered because of that."