Burnley midfielder David Jones has signed a new two-year contract.
Arsenal goalkeeper Wojciech Szczesny has joined Roma on a season-long loan deal.
Hackett, 29, made 145 appearances for the Lions, scoring five goals, since joining from Hearts in 2006.
However, he slipped out of the first-team picture this season and ended the campaign on loan at Wycombe.
Former Leicester and Watford full-back Stewart, 30, endured an injury-hit season since he signed last summer and managed just seven appearances.
Youngsters Jake Gallagher and Conor McLaren have also been released.