The 24-year-old has signed until the summer of 2018 after joining from ITM Cup side Counties Manukau. He also made two appearances for the Chiefs in Super Rugby last season.
Firth said: “This is a great opportunity for me and I’m delighted to sign a long-term contract with the Warriors.
“Everyone I spoke to had great things to say about the club and the city, so I jumped at the chance to get over here.
“Glasgow have had a few Kiwis before and they’ve always done well, so there is no reason why I can’t be successful too.
“I played against Grayson (Hart) in my younger days and it’s good to see him doing well here.
“It’s good to get in and meet everyone and I’m here now and ready to go and hopefully I can earn the chance to pull on the jersey.”
Warriors head coach Gregor Townsend said: “We’ve been tracking Jarrod for some time in the ITM Cup and he’s built a very good reputation as a strong scrummager.
“Initially he’ll be working with our conditioning staff as we start to get him integrated into the rugby we aspire to play.
“Jarrod has made a big commitment in coming to Scotland and we believe he’ll fit in really well at Scotstoun and add further competition in our front-row.”