The 29-year-old started his senior rugby career with Plymouth Albion and scored 45 tries in 111 games for Bristol following his move there in 2005.
At 6ft 2in tall and weighing 17 stones, Robinson is a powerful finisher who enjoyed four seasons of Premiership rugby with Bristol up to last summer.
Tigers head coach Richard Cockerill said: “Lee has a good strike-rate from the wing and has a good physical presence in attack and defence. We look forward to his arrival for pre-season.”
Robinson scored 12 tries in 24 starts for the Championship club in 2009/10 as Bristol reached the promotion play-offs before suffering defeat over two legs by Exeter Chiefs.
He said: “It’s obviously disappointing to finish the season the way we did at Bristol, but this is a new challenge at a massive club and it is one I am looking forward to.
“I met the coaching staff and had a look around at Leicester, I was very impressed with the set-up and I am very happy to make the move to Tigers.”