
City had tried to pull out of the deal initially, saying they had concerns about the striker's fitness but the move went through on Tuesday with Benjani signing a two-and-a-half year deal.
Portsmouth will receive 3.87 million pounds (7.6 million dollars) for Benjani, a fee that could rise to 7.6 million pounds, if he makes 75 senior starts for the club.
"I'm delighted we have signed such a quality player, and I am looking forward to working with him," Manchester City manager Sven-Goran Eriksson said.
Portsmouth's director of communications, Gary Double, said there were no problems with Benjani's fitness.
"It's good to get this sorted for both clubs and of course for Benji, who is the most important person in this," he said.
"Manchester City are concerned about Benji's knee, whereas both Portsmouth and Benji know there's not a problem.
"He's as strong as an ox and never misses a day's training, but in order for the deal to go through for Benji we've agreed to phase the payments."
Portsmouth signed Tottenham striker Jermain Defoe on transfer deadline day, in the knowledge that Benjani would be moving to City.