The Centurions have been busy tying down some of their current players to new contracts, and this follows hot on the heels of the re-signing of half-back Martyn Ridyard on a two-year deal.
Littler, 33, joined Leigh at the beginning of last season after spending 13 years at Salford, where he scored 112 tries in 329 appearances.
He has signed a two-year deal, while former Bradford and Warrington prop Parker has signed a one-year extension.
Head Coach Paul Rowley told the club’s official website: “Stuart and Rob are two vastly experienced and successful players, who are not only great on the field, but offer just as much off of it.
“My strategy of having the right experienced players is evident, and I’m delighted to retain the services of Stuart and Rob.”