The 20-year-old, who is a part of England's Six Nations squad, has agreed a two-year contact at Kingsholm, which will begin in July.
"He's been influential in all the teams he's played for. As an out-and-out seven he's one of the best out there at the moment. He's also a leader and in successful teams you need leaders on the park," Davies told BBC Sport.
"He's a young boy who is one of the rising stars in English rugby and for us to sign him is a big statement of intent."