Puletua, 34, announced his departure on his Twitter page, following newspaper reports that he had signed a two-year deal with the City Reds for 2014.
He tweeted: “To all the Saints fans. Thank you so much for the support over the years here at this great club. It’s been an honor! (sic)
“I apologise about the announcement coming out in the papers before I said anything. It’s not how I wanted it to happen.”
He has made 130 appearances for the club, scoring 40 tries, and will follow team-mate Francis Meli to the Salford City Stadium.