He joins on a two-year deal, subject to visa and medical.
The 28-year-old spent two years at Allianz Park, having signed from Zebre in 2015.
Fijian-born Vunisa qualified for Italy through residency and has gone on to play 11 times for the Azzurri and was a member of their 2015 Rugby World Cup squad.
Capable of playing across the back-row and renowned for his hard ball carrying, Vunisa began his playing career in New Zealand playing for Taranaki in the Mitre 10 Cup.
In 2011 he joined Italian side Calvisano, spending two-and-a-half years there and crossing the whitewash 19 times in 48 appearances.
He played 43 times for Zebre and scored eight tries, before moving to the English Premiership, where he has played 13 times for Saracens and scored six tries.
Vunisa will join up with his new teammates at Scotstoun for the start of pre-season training in June.
Speaking to glasgowwarriors.org, Samuela Vunisa said: "It's really exciting, I enjoyed my time in the PRO12 before and I can't wait to get started with the Warriors.
"Glasgow has made a name for themselves. Winning the PRO12 and reached the Quarter Finals in Europe shows that on and off the field it's a great club and I'm looking forward to being a part of it.
"Dave Rennie is a world class coach, he is respected in New Zealand and across the world. I'm looking forward to working with him as I know he'll get the best out of me."
Glasgow Warriors assistant coach Jonathan Humphreys added: "Samuela is a strong runner and ball carrier and will add to our strength-in-depth in the backrow.
"He joins us form a winning environment and has played at the highest level on the international stage.
"We're delighted he has decided to join us and we look forward to seeing him continue to develop in Glasgow."