But the Israeli midfielder may come back immediately to haunt Kevin Keegan as he could be making his debut for Portsmouth on Saturday against City.
Keegan had wanted to ensure this would not happen but Pompey chairman, Milan Mandaric, threatened to pull out if such an agreement was struck.
Berkovic said: "All I want to do is get down to playing football regularly again and help the club out of the bottom three which I believe I can."
Pompey boss, Harry Redkanpp, told BBC Sport: "He can be moody and he has his own mind, but the little fella can play and create."
"I had three or four fantastic seasons with him at West Ham and I'm sure he'll make us play."
Redknapp added: "He can create. I'd rather get someone in like that rather than one who will win 50 tackles and give the ball to the opposition 49 times."
Clearly Kevin Keegan feels City don't need anyone like that.