The Premier League champions agreed a deal for the 21-year-old back in May.
Haaland has signed a five-year contract lasting until the summer of 2027.
The Norwegian is one of Europe's most fearsome forwards, having scored 86 goals in 89 appearances for Dortmund after joining from RB Salzburg in December 2019.
Haaland's father, Alf-Inge, also played for Manchester City between 2000 and 2003.
"This is a proud day for me and my family. I have always watched Man City and have loved doing so in recent seasons," Haaland told Man City's official media channels.
"You can't help but admire their style of play, it’s exciting and they create a lot of chances, which is perfect for a player like me.
“There are so many world-class players in this squad and Pep is one of the greatest managers of all-time, so I believe I am in the right place to fulfil my ambitions.
“I want to score goals, win trophies, and improve as a footballer and I am confident I can do that here. This is a great move for me, and I can't wait to get started in pre-season.”
Man City's director of football Txiki Begiristain added: “Erling has everything we want in a striker, and we are certain he will excel in this squad and this system."
“His rise has been remarkable, but he is still only 21. His best years are ahead of him, and we are confident he can get even better working with Pep.
“This is a very exciting signing for our club, and I am sure our fans will enjoy watching Erling perform in this team.”
