A former Wales age-group international, Roberts moved to Rotherham at the start of the 2013/14 season after previous experience Welsh Premiership outfit Llandovery.
Roberts, 22, was an important part of the Rotherham squad that reached the Championship play-offs last season and played in last weekend’s 31-29 win over Ulster Ravens in the British & Irish Cup.
Tigers director of rugby Richard Cockerill said: “Jack is a young and ambitious player who we have seen play well in Championship company for Rotherham. Now he has an opportunity to take that potential into an Aviva Premiership club and we look forward to working with him.”
Titans head coach Lee Blackett said: “It’s obviously massively disappointing to lose a player who is as good as Jack Roberts.
"It’s disappointing for us a club but it’s great for Jack and it’s an opportunity for him to show how good a player he his.
"He’s given the club 100 per cent during his time at Clifton Lane and as a club we are very proud of how he’s developed during his time here and we wish him all the best at Leicester Tigers.
“He’s done a fantastic job for the Titans and for me he is destined to reach the top; there can be little doubt about that.
"I think it was obvious to everyone within the club that Jack Roberts wasn’t going to be here at the end of the season, the guy is a Premiership rugby player and we all wish him every success.”