The highly-rated Croatia defender moves to England after two seasons in Germany.
The European champions have paid £77m to sign the 21-year-old.
Gvardiol is Manchester City's second summer signing, joining compatriot Mateo Kovacic in making a move to the Etihad Stadium.
Gvardiol made 87 appearances in his two seasons with Leipzig, scoring five goals and winning two DFB-Pokal trophies.
He has been capped 21 times by the Croatia national team and played an instrumental role in their run to the FIFA World Cup semi-finals back in December.
The former Dinamo Zagreb defender told City's website: "I have always dreamed of one day playing in England and to be doing so now with Manchester City - after the season they have just had - is a real honour for me.
"Anyone who saw Manchester City play last season knows they are the best team in the world. To win the treble says everything you need to know about the quality this team has.
"To be joining City is something very special for me and my family. To have the chance to work with Pep Guardiola will be amazing. I know I am not yet the finished article and I am sure my game will progress under the best coach in football.
"To be linking up with Mateo Kovacic will also be special. He's a top footballer and I hope we can both help City achieve another successful season in 2023/24 and then beyond."
Txiki Begiristain, City's director of football, added: "We are very happy to bring Josko to Manchester City. He is a player we have watched closely and we feel he has a superb set of attributes.
"Top clubs all over Europe have been monitoring him so to bring him here is great news for us.
"Josko has so many qualities - everything you want in a centre-half. He is fast, competitive, combative, strong in the air, impressive in possession of the ball, with strong self-belief and a good character. He is left-footed, too, which offers us good options at the back.
"He is still young but his progress in the game has been rapid. We feel confident his upward trajectory will continue here at City working with Pep and his staff."
