The 26-year-old has 16 caps and has scored 55 Test points since making his All Blacks debut against South Africa in July 2015.
In the same year, Sopoaga helped guide the Highlanders to their first Super Rugby title, and has made 74 appearances for the Dunedin-based franchise since his 2011 debut.
The exciting fly-half claimed the Highlanders’ seasonal points-scoring record in 2015 when he amassed 191, and is also second-ranked in the franchise’s history for most career points with 701.
Sopoaga also represents Southland in New Zealand’s Provincial Rugby Championship. He joined them from Wellington in 2014 after scoring all his native province’s points in their 2013 final defeat by Canterbury.
Sopoaga was part of New Zealand’s U20 side that retained the junior IRB World Championship title in 2011, where he appeared alongside back-rower Brad Shields, with whom he will be reunited at Wasps next season.
Wasps director of rugby Dai Young said: “When a world-class fly half became available we jumped at the chance, as that doesn’t happen very often.
“Lima’s track record with the All Blacks, Highlanders and Southland speaks for itself, and we believe he will be an extremely good fit both in our side and within the club.
“A big part of my job is to continually find ways to move things forward, both by developing our current players and when the opportunity arises adding to the squad, and I am confident this signing does this.”