O'Dea's deal with the npower Championship club was due to expire after Saturday's game with Millwall, while the change in manager at Portman Road also left his future uncertain.
However, Celtic agreed the Republic of Ireland international could stay with Town until the end of the current campaign.
Ipswich manager Paul Jewell, who has succeeded Roy Keane as boss, told the club's official website, www.itfc.co.uk: "The deal was agreed before I came here for Darren to stay and I'm happy with that."
Jewell also plans to take to Plymouth manager Peter Reid about Rory Fallon's loan deal, which is due to end next week.
Source: PA
Source: PA