The 35-year-old Trinidad and Tobago international, who spent the last two months of the season on loan at Millwall, has signed a one-year deal with the Londoners following the expiry of his contract at Portman Road.
The right-back struck the winner at Wigan on April 8 that lifted Millwall out of the bottom three. Ian Holloway's side finished four points above the relegation zone after closing the season with an eight-match unbeaten run.
"For me it was really exciting because we were playing good football and getting wins and draws every game, so I was enjoying myself," Edwards told Millwall's official website.
"To stay up was great and now I'm delighted to be joining the club on a permanent basis and really looking forward to next season."
Edwards joined Ipswich from Sunderland in August 2009 and made 191 appearances, scoring 10 goals.
He was made skipper by former Ipswich boss Paul Jewell but was restricted to 10 appearances for Ipswich last season.