A fee of £200,000 has been paid by Celtic to Southampton.
Meanwhile, former City keeper Magnus Hedman has left Celtic. The Swede joined the Scottish giants from City three years ago for £1.5m but could not a regular first team place.
Celtic have released a statement saying: "Celtic Football Club confirms that Magnus Hedman's contract with the club was brought to an end with effect from June 30th 2005, by agreement between the player and the club. "The club is grateful for Magnus' contribution to the team's success in recent years and wishes him well in his future playing career."