The deal will keep the 34-year-old former England international with the Tractor Boys at least until the end of the season.
Wright left Ipswich for Arsenal in a £6million deal in 2001.
Town boss Paul Jewell told the club’s official website: “Richard has been training with us this season and has done well. He has looked really sharp over the last few weeks.
“I know there were two or three clubs interested in taking him on this week so we’ve been speaking to him over the last day or so and I’m delighted that we’ve been able to agree a deal.”
