Twenty-eight-year-old Stewart and Qualter, 26, both arrive from manager Craig Elliott's former club, Evo-Stik League Premier outfit Shaw Lane AFC, following the completion of an agreement between the two clubs.
Both players have previous experience of National League North following spells with Bradford Park Avenue, while Stewart has also appeared for Alfreton Town.
Stewart (pictured) has also played under Eddie Howe at AFC Bournemouth and Burnley.
Qualter, meanwhile, is a centre-half by trade and has plenty of experience at Steps 2 and 3 of the non-League Pyramid.
Both players will be eligible to make their Pilgrims debuts against Tamworth today.