Bristow last season made 21 appearances for Welsh in the Aviva Premiership.
He told www.leicestertigers.com: "I enjoyed my experience with London Welsh in the Aviva Premiership last season but I'm happy to be here now and delighted to have the opportunity with Leicester Tigers.
"I'm looking forward to settling in during the pre-season and being part of the Tigers squad."
Leicester director of rugby Richard Cockerill said: "Tom is a young up-and-coming prop and he joins a very good bunch of promising young front rows at the club, including Fraser Balmain, Ryan Bower and academy prospects Riccardo Brugnara, Tiziano Pasquali and Harry Rudkin."
- Sports & Recreation
- Leicester Tigers
- Aviva Premiership
- Richard Cockerill