The 25-year-old will join the Aviva Premiership club at the end of the current season.
Leiua, who has won four caps for his country, is able to play both at centre and on the wing.
"We have been really impressed with what we have seen of Alapati and he will add power and pace to our backline options," Wasps director of rugby Dai Young told the club's official website.
"We have identified the type of players we need to add to the side and he fits the bill very well. He is powerful, has good feet and knows where the try line is, and I am sure he will make a big impact here."
Wasps are back in action on Saturday when they host Newcastle Falcons in the Aviva Premiership.