The 30-year-old, who will arrive following the conclusion of the Super Rugby Season, has played 91 times for the Chiefs and won two Super Rugby titles under incoming Warriors coach Dave Rennie in 2012 and 2013.
Capped for the All Blacks, Masaga scored 38 tries in Super Rugby before moving to Japan and has since returned to the Chiefs wider training squad this season.
Nicknamed 'Flash', Masaga also played 65 times in the Mitre 10 Cup during his time in New Zealand, scoring 28 tries for Counties Manukau and Bay of Plenty.
"I'm looking forward to being there under Dave Rennie as head coach, to be part of a great team of players and to meet all the fans who support the club.
"I can't wait to start this new journey in Scotland."
Glasgow Warriors incoming assistant coach, Jason O'Halloran added: "Lelia is an experienced and powerful player who has proven himself at the highest level in Super Rugby.
"He knows Dave (Rennie) well through their time together at the Chiefs and will be an excellent addition to our squad."