Stewart (28) and Qualter (26) both arrive from manager Craig Elliott's former club Shaw Lane 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 (pictured) has appeared for Alfreton Town too.
Stewart has also played under Eddie Howe at 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 United debuts against Tamworth on Saturday.