The 21-year-old joined Tigers on loan in February, making five appearances, and is one of four uncapped players in the England squad for the summer Tests.
Genge made his senior debut for Bristol in the 2013-14 British and Irish Cup, and scored six tries in 26 appearances.
“Ellis has made a big impression in his time on loan with us,” said Leicester director of rugby Richard Cockerill.
“He is a great young prospect and he seems to have found his home at Leicester in his time on loan with us.
“We hope he continues to build on that first impression and we look forward to seeing his development here.”
Genge is in the England squad both for Saturday’s Test at home to Wales and the June tour of Australia.