The 22-year-old, who is a full England international, has been branded "a very impressive individual" by Middleton.
"Ben is a very impressive individual with a wealth of experience," Middleton told Bristol's official website.
"He's a widely respected professional who can become an integral member of our squad. Ben is a powerful ball-carrier, a hard worker and gives us plenty of options in the lineout.
"We're trying to build a squad with the right balance of youth and experience - Ben fits the bill of a player in the prime of his career."
Skirving, who will join Bristol at the end of the season, came through the academy at Saracens.