The Bulgaria winger, 28, sealed a three-year deal at Eastlands following a £4.7million move from Atletico Madrid.
City won the race to secure his signature ahead of a number of European clubs.
He looked set at one stage to link up with international team-mate Dimitar Berbatov at Tottenham.
Petrov gave his reasons for his choice after being unveiled at a press conference at the club's Carrington training ground.
"The Premier League is the best league in the world and the best competition," he said.
"But the main reason I have joined Manchester City is because of the manager. That's why I have made this decision."
City chief executive Alistair Mackintosh added on the club website: "Unsurprisingly given the calibre of the player, there were a significant number of clubs competing for Martin's signature.
"Having Sven-Goran Eriksson as our manager proved to be a major factor in the player's decision to move here."
Petrov is a regular for Bulgaria, with more than 60 caps to his name, and was allowed to leave the Vicente Calderon as Atletico line up Benfica winger Simao Sabrosa.
He is Eriksson's fourth signing since he took charge and follows £8.8million striker Rolando Bianchi, Gelson Fernandes and Geovanni to the club.
Former Barcelona and Benfica midfielder Geovanni was also presented to the media alongside Petrov and Eriksson said: "I am sure a lot of clubs wanted both players.
"But the board here have backed me and they will do very well for us.
"Both of them bring a lot of experience to the squad as between them they have played a lot of international matches. They are also very good technically.
"It is important we do not just buy players who are 19, 20 and 21. You need to balance it up."
Petrov has been compared to Bulgarian legend Hristo Stoichkov but Eriksson said: "I think we should only look at what Martin does himself.
"He will have a lot of chances to show the supporters what he can do. I am quite confident he will do well."
With Eriksson acting as his interpreter, Geovanni said: "I am impressed by the facilities here and hopefully the team can have a good season."
The Brazilian, who returned home to play for Cruzeiro last season, is set to make his debut for the club on Saturday against Charleroi in Belgium.
City struggled for goals in the last campaign and that is one area the former England coach has been quick to address. He wants to improve the line of supply to the strikers.
Eriksson said: "We are working every day on the training pitch and want to play good football.
"Wingers are also important in my mind. You need players who can dribble and cross.
"It is nothing new. You want balls to come into the area."
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