Haaland, 21, put pen to paper on a five-year deal at the Etihad Stadium.
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Haaland said: "This is a proud day for me and my family. I have always watched City and have loved doing so in recent seasons. 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 fulfill 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 preseason."
HE'S HERE! 💙 pic.twitter.com/JuZEtzTWbv— Manchester City (@ManCity) June 13, 2022
Earlier in May, City confirmed a deal with the Bundesliga club had been agreed to sign the striker after paying a release clause of €60 million ($64m), according to ESPN sources.
Haaland joined Dortmund from Red Bull Salzburg in January 2020 and scored 41 goals in 41 games in his first full season. At international level with Norway, he has scored 20 goals in 21 games after making his debut in 2019. He scored 36 goals in 34 appearances for club and country this season.
City director of football Txiki Begiristain added: "We have been monitoring Erling for several years now, so we are delighted to bring him here to Manchester City.
"He is a huge talent and has been one of the best strikers in Europe over the last few seasons. His goal scoring record is exceptional and his performances at Borussia Dortmund and in the Champions League in particular have proved he can succeed at the highest level.
"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."
Haaland will be key addition to Pep Guardiola's team as they look to become the first side to win the league for a third consecutive season since Manchester United in 2009.