The 22-year-old lock has been capped by England in three age groups and made his senior debut for Leicester Tigers in January 2013.
The all-round sportsman played his junior rugby with Stratford Upon Avon RFC and Kineton High School and represented Warwickshire through the age grades. Price, like Scarlets' second row Jake Ball, is a keen cricketer and played Warwickshire District cricket and won a schools' county football title.
With second rows Ball and George Earle already signed on the dotted line and confirmed as staying at the Scarlets, Welsh qualified Price will be mentored by quality locks as he looks to develop further in the senior environment.
Scarlets Head Coach Wayne Pivac said: "Tom is an exciting young prospect that will add another dimension to our second rows here at Parc y Scarlets. He has experience at under 20s level with England but is looking for an opportunity to flourish and break into senior rugby which we're excited to offer him here."
Price added: "The Scarlets pack has developed into a formidable force in the last few seasons and I'm looking forward to being a part of that onward journey.
"When the opportunity came to look at alternatives for my playing career going forward Scarlets, as a club that is steeped in history, interested me as it's similar to Leicester in so many ways.
"I'd like to thank the coaches and staff at Leicester Tigers who've supported me through my early career. I feel the time is right for me personally to make a move and hopefully have an opportunity to break into the senior side."
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