Toomaga-Allen, who played his only test against Japan in 2013, has not been able to crack the national squad over the past 12 months, despite regularly featuring at All Blacks camps as cover or as a squad member.
The 28-year-old was named in the 2017 Rugby Championships squad, and played against the Barbarians and French XV on the northern tour that same year, but never got the chance to add to his sole test cap.
"I'm really excited to be joining Wasps later this year," Toomaga-Allen told the Wasps website. "It's a fantastic club with a lot of history.
"I want to help the club compete at the very top of the Premiership and European competitions, and hopefully I can be part of something special in winning trophies."
Wasps director of rugby Dai Young said: "To bring someone of Jeff's calibre to the club is fantastic news.
"Jeff is a solid scrummager, while also being strong in defence, and like most New Zealanders, he is gifted with ball in hand, so he's a terrific all-around player.
"We're looking forward to him joining us next season, as he'll provide a real wealth of experience to the front row."
He is the second All Black signed by Wasps this week, following the capture of midfield Malakai Fekitoa from Toulon.
Toomaga-Allen will link up with former Hurricanes teammate Brad Shields at Wasps - both made their Super Rugby debuts in 2012 and both also reached the 100-game milestone for the franchise in 2018.
Former All Blacks first-five Lima Sopoaga is also contracted to the club, along with former Hurricanes and Blues pivot Jimmy Gopperth.
Toomaga-Allen will make the move to England after the Super Rugby season, along with Hurricanes teammate Matt Proctor, who will join former coach Chris Boyd at Northampton.