Scrum-half Cliff, 28, came through Sale's academy and made 113 appearances before leaving in March 2015.
Hooker Jones, 29, joined Bristol in the same year and helped them to promotion from the Championship in 2015-16.
"It's great news for the club," Sale director of rugby Steve Diamond said. "They both know what we are about, the culture and where we want to be."
The Sharks are 10th in the Premiership, 12 points clear of bottom-of-the-table Bristol.
The pair will join Glasgow Warriors forward Josh Strauss at the club next season, after the Scotland international agreed a three-year deal in February, and Diamond is expecting more arrivals.
He added: "Our signing programme is moving along nicely and we are just awaiting news on work permits and visas before we are able to announce some international signings."
Sale Sharks have re-signed Will Cliff and Marc Jones from Bristol ahead of next season on two-year contracts.