Edwards has been without a permanent club since Peter Taylor terminated his contract in March, failing to make one appearance since Taylor took over the reigns at City.
He then joined Colchester until the end of the season, making five appearances, but despite impressing manager Phil Parkinson, his contract was not extended.
Hull-born Edwards had previously made over 200 appearances for City since coming through the youth system at Boothferry Park.
Meanwhile, fellow ex-Tigers Lee Philpott and Jamie Wood have also found new clubs. Midfielder Philpott - who was released on a free transfer last month after three years here - has joined non-league Weymouth. Wood - a City forward in 1999-2001 before spells at Halifax and Swansea - has gone to Welsh side Total Network Solutions, where fellow ex-Tiger Gary Brabin is also currently playing.