City has agreed a five-year contract with the Palmeiras winger believed to be worth £27 million ($36 million).
There are also add-ons which could total £4 million ($5.3 million), depending on his Premiership performance next season - but he will not join the club until after December.
In a press release from City announcing the signing, Jesus said:
"Manchester City is one of the best clubs in the world so I'm really pleased to sign. We have many great talents in the team and a fantastic manager in Pep Guardiola that I can learn so much from. I'm looking forward to showing the City fans what I can do and I think we'll have a great future together!"
City fans can check out Jesus' skills when he plays for his native Brazil at the upcoming Rio Olympics. He has an excellent record at Palmeiras, scoring 14 goals in just 32 appearances. He was also voted the Campeonato Brasileiro Série A Best Newcomer in 2015.
Here he is in action:
The signing comes hot on the heels City announcing Leroy Sane's transfer to the club, for £37 million ($49 million). City's Premier League begins with a home game against Sunderland on August 13.