Williams joins Dave Lewis who signed from Exeter in February on a one-year deal. The 18-year-old can play at either lock or blindside.
"It has been made very clear in all of the signings Dean Ryan has made so far that the quality of the facilities on offer at Hartpury - on an off the field - have been instrumental and we think Dan is in the perfect environment to further his education and rugby career," Cornwell said.
"The club made a major statement last season with the development of young, talented and determined players, and Dan and Dave represent the next tier coming through.
Williams, who joins from Ivybridge College in Devon, will begin his contract in the summer.
Meanwhile, hard-running centre Ali James, who has been playing for Newbury this season in National League One, rejoins Gloucester on a one-year contract.
The former Oxford University student was part of the Gloucester squad two years ago and returns to increase Dean Ryan's options at 12 and 13.
"The season with Newbury was just what I needed to get some game-time under my belt in a tough league," James said.
"I'm ready now to get back into the Premiership environment and hopefully force my way into contention for selection."