The star striker has penned a deal to 2034 in what could be Begiristain's most important achievement in his final six months in charge.
The Spaniard will be leaving at the end of the season and said: "Everyone at the Club is absolutely delighted that Erling has signed his new contract. The fact he is signed for so long demonstrates our commitment to him as a player, and his love of this club.
“He has made an incredible impact already in his time here and his amazing numbers and records speak for themselves.
“But in addition to his outstanding natural talent and ability, Erling’s dedication, professionalism, humility and desire to keep getting better sum up what we all strive to achieve at Manchester City.
“He is one of the finest strikers in world football, but Erling is still very young and will only continue to improve working under Pep and his coaching team. If he works hard, which I know he will, he will create an incredible legacy at this football club.
“Now he can focus on his game and continuing to play a huge part in helping us try to achieve even more success.”