The 28-year-old, who can also play full back, has played 58 times for the Crusaders and is in line to make his 71st provincial appearance for Canterbury this weekend.
Hamilton's last appearance in an All Black shirt came in the Tri Nations win over South Africa in Wellington in 2006, with his try-scoring debut being the match against Argentina in Buenos Aires earlier that year.
"Scott is a very important senior member of our team and we'll miss him a lot," said Canterbury coach Rob Penney.
"As a player of some ability and profile, Scott is a great role model for all our players here and he's a great character to have on the field and dressing room."
Leicester have been searching for a winger all summer, with reports previously linking the 2077 Guinness Premiership finalists with Leeds Carnegie youngster Tom Biggs and new London Irish signing James Bailey.
The East Midlands club have also been in talks with Fijian star Rupeni Caucaunibuca and, although the move has stalled, head coach Meyer has not yet ruled out bringing Caucau to Welford Road.
"We are no further than we were three weeks ago," said Meyer when talking to the Leicester Mercury about the Fijian.
"I need guys to fit in and want to be here. We have not offered him a contract. It's more a question of 'if you want to be here, come over for a trial period'.
"He has had problems with visas and other problems as well. That why I always like to have one or two other options. If you just bank on one option, you are in trouble."