The opening months of Newcastle's 2008–09 season were blighted by ownership and managerial turmoil, as well as numerous injury problems. This manifested itself on the pitch as the club struggled to direct itself clear of the relegation zone. However a highlight was Given saving a Kevin Nolan penalty in a 1–0 win over Bolton Wanderers. On 2 January 2009, following the 5–1 defeat at home against Liverpool, the player's lawyer released a statement saying that his client was "considering his future" at Newcastle, and requested permission to talk to representatives of Manchester City on 28 January after the club made a bid of £5 million which was subsequently rejected. Newcastle manager Joe Kinnear had already stated that the club was "not interested at all in selling him", and described the amount on offer for Given as "insulting". However, on 30 January, it was reported that Newcastle had given permission for Given to enter talks with his suitors. After a transfer fee initially reported to be around £8 million was agreed between the clubs, Given signed for Manchester City on 1 February, with the transfer window set to close the following day. The news was disappointing for Newcastle fans who felt that Given left the club in a poor situation with many thinking that had Given delayed his decision to leave until the summer, Newcastle would have subsequently survived relegation to the Championship because Given was such a fantastic goalkeeper who could have stopped many of the goals that the Toon conceded towards the end of the dreadful campaign. Although the fee for Given was expected to be around £8 million, in February 2009 Newcastle United managing director Derek Llambias revealed at a supporters panel meeting that Given had been sold for an initial £5.9 million. Given was 34 games away from breaking Newcastle United's appearance record held by Jimmy Lawrence.
On 1 February 2009, Given signed for Manchester City on a four-and-a-half-year contract for £6 million. He was formally paraded as a Manchester City player on 5 February 2009, and was assigned squad number 37. In the subsequent press conference, he criticised Newcastle's management for not trying hard enough to keep him at the club. He also said that "By coming here I thought I could be at a club that is challenging for honours. I didn't want to finish my career regretting not taking up this offer." Given kept a clean sheet in a man of the match performance in his debut, a 1–0 win against Middlesbrough on 7 February.
With Joe Hart leaving the club on loan, Given was given the squad number 1 for the 2009–10 season. He made his 400th league appearance on 5 October 2009 against Aston Villa. On 1 November 2009, he saved a James McFadden penalty to help his side draw 0–0 at Birmingham City. On 5 December 2009, he made an outstanding penalty save from Frank Lampard to deny Chelsea an equalising goal. City went on to win 2–1. The same month, Daily Telegraph football correspondent Henry Winter named Given as Premier League Goalkeeper of the Noughties. While team captain Kolo Touré was on international duty, Given was given the captain's armband by manager Roberto Mancini, who described the Donegal-born player as "one of the five best goalkeepers in the world". He dislocated his shoulder during a match against Arsenal on 24 April, ruling him out for the rest of the season.