Scrum-half Commins has signed on from Northampton Saints, where he made 17 appearances this season, while centre Hayter has arrived from RFU Championship side Moseley.
"These are two positions in which we needed to add depth. We're losing two centres – Andrea Masi and Elliot Daly – to international duty in the coming weeks and with a long-term injury to Lee Thomas, adding another centre to the squad was important," said director of rugby Dai Young.
"Charlie has been very good at Championship level so we're looking forward to seeing what he can do. With Joe Simpson with the England Saxons for a few weeks combined with the fact that we haven't replaced Nic Berry, who retired earlier in the season, we also needed another scrum-half and Stuart has good experience and has fitted in well so far."
Both players will go into the squad for the weekend's clash against Leicester Tigers.