The 27-year-old has not played a game this season, with his efforts to return from a broken ankle suffered in last term's semi-final defeat by Bath hampered by a foot problem.
Morris has scored 18 tries in 75 games since joining from Leinster in 2011.
"He's out of contract at the end of the season and he will move on," director of rugby Richard Cockerill said.
"He's had injuries and we have recruited in the back three, so there is no room at the table.
"Niall will make a full recovery from his injury and I'm sure he will find another club to play for.
"He's been good for the club, a great player and we wish him well."
While Morris, fellow versatile back Niki Goneva and Argentina wing Gonzalo Camacho are to leave Welford Road, South Africa international JP Pietersen and Sales' Tom Brady are joining the Tigers for the 2016-17 season.
Injury-plagued back Niall Morris will leave Leicester Tigers at the end of the season.