Edwards, 34, moved to the Tractor Boys in 2009 and agreed a new one-year deal with the club last season.
The deal had the option of a further year based on appearances and this has now been activated.
He will play his part in Mick McCarthy's fight to retain Championship status this season and then push on next term.
But 31-year-old Ellington has departed the club by mutual consent after the striker, who moved to Portman Road in the summer of 2011 on a two year deal, made only 19 appearances, with only three starts.
Ellington told the club's official website: "It hasn't really worked out for me at Ipswich for one reason or another but I wish the club all the best for the future.
"Mick McCarthy is a terrific manager and treats you with respect. He has been great to me since he arrived at the club and Ipswich are in good hands with him in charge.
"It's a terrific football club but it's the right decision for me to move on. I still want to carry on playing and have already started looking for a new club."