The 21-year-old, who has been capped by Wales at Under-20 level, will move to Welford Road in the summer.
Before opting to move to the Aviva Premiership, Williams had been offered a senior contract at the Parc y Scarlets.
Scarlets head coach Simon Easterby said: "Owen Williams has been on our development pathway for a number of years and is another example of a young player we have invested in and that has progressed well within our system - highlighted by his involvement with the senior squad this season.
"We had fully expected him to continue on that journey with us following the significant commitment this region has made in developing his rugby skills and experience to date.
"We have handed him some excellent opportunities recently this season which he has taken very well and which we believed showed our intent to develop him further as a Scarlets player.
"However, sometimes performances on the bigger stages bring with it additional attention from outside our group and he along with his agent have made his decision to move to England at this time at the end of his development contract with us.
"Of course, Owen goes with our very best wishes for the future and we wish him every success. He is still a young Welsh player with a lot to experience and prove and in making this decision we sincerely hope he gains from his time at a Premiership club."
Williams has made seven appearances for the Scarlets this season.