The 25-year-old, who has been capped 38 times at international level, was released by Sale earlier this year following an injury-hit spell in the north west.
Leicester director of rugby Richard Cockerill is confident Tait has much to offer the club.
"We think Mathew is an excellent addition to the squad," he said.
"He has gained a lot of experience for a player who is still just 25 years old and he has played at the highest level, including the World Cup Final in 2007.
"But he is still young, he is still ambitious and he wants to challenge himself here."
Tait, who has also played for Newcastle Falcons, is looking forward to a new challenge after a frustrating time with Sale during which he suffered a knee injury and a dislocated shoulder.
"The move to Leicester Tigers gives me a great opportunity to continue my development as a player and I know there is still a lot to come in my career," said Tait, who can also play at wing and full-back.
"I've enjoyed some great times in the game already and I still have ambitions and goals to achieve in rugby.
"There is a superb set-up at Leicester and a very competitive squad. I'm looking forward to trying to establish myself in the team here."
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