The 22-year-old, who can play wing or full-back, has previously played for Blackrock College as well as appearing in the Celtic League and British & Irish Cup with Leinster during the last two seasons.
Capped by Ireland at age-group level, Morris joins countrymen Geordan Murphy and Jeremy Staunton in the Tigers squad ahead of the 2011/12 season.
He said: “I enjoyed my time with Leinster. I’d been there a long time, but this is a new challenge for me and I’m looking forward to it.
“I spoke to Shane Jennings and Leo Cullen, and they had nothing but good things to say about the Tigers, and Geordan Murphy has been very good in showing me around the place.
“There are players away with national squads but it's still a competitive squad. Now I just want to work as hard as I can and take whatever opportunities I can here.”
Director of rugby Richard Cockerill said: “Niall is a good all-round footballer, he’s aggressive, he’s got some pace. He’s come from a good environment and we think he’ll settle here very quickly.”
Morris has already played at Welford Road, as part of the Leinster squad in last summer's pre-season fixture against Tigers, a match won 37-14 by the hosts.
You can hear more from Niall Morris in an LTTV interview on the Tigers website on Friday morning.