The 32-year-old has reached an agreement over money outstanding for the final year of his contract and has walked away from Fratton Park without another club to go to.
Administrator Trevor Birch told the club's official website: "I'd like to thank Dave and his agent for the stance they've taken to give Portsmouth Football Club the best possible chance of survival. We thank Dave for his service to the club and wish him every success for the future."
Kitson made 72 appearances for Pompey after arriving from Stoke in August 2010, scoring a total of 12 goals.
His departure is a big boost in the club's fight for survival and leaves Tal Ben Haim and Liam Lawrence as the only high-wage earners who need to be sold before August 10.