The Bulgaria winger, 28, sealed a three-year deal at Eastlands following a £4.7million move from Atletico Madrid.
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.
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."