The 21-year-old has been on trial at Scotstoun and impressed head coach Danny Wilson sufficiently to be offered a deal.
Unlike McKay, Forbes is Scottish qualified but like his compatriot he has experience of playing at stand-off, although Wilson sees him more as a wing or full-back.
Glasgow say he has signed “a multi-year deal”.
“Cole has really impressed us since joining in January,” said Wilson.
“He’s a back-three player with pace, good footwork and has shown a defensive physical presence already in training.
“He joins us with experience playing in the Mitre10 Cup and has previously represented New Zealand Under-20s.
“Cole has worked hard in training and shown a lot of promise. We look forward to seeing what he can do in the Warriors jersey.”
Born in Pukekohe in the Auckland Region of the North Island, Forbes first caught the eye when helping Bay of Plenty to the Jock Hobbs Memorial National Under-19 tournament in New Zealand, before going on to make his senior debut for the province in the Mitre10 Cup.
Scottish-qualified through his grandfather, Forbes was part of the New Zealand squad which finished fifth at the 2019 World Rugby Under-20 Championship.
Forbes said that former Glasgow Warriors player Hugh Blake helped pave the way for his move to Scotland.
“Hugh Blake and I played Mitre10 together for Bay of Plenty, and he got me in contact with an agent up here,” Forbes told glasgowwarriors.org.
“They put me in touch with Danny and the coaches at Glasgow, who were keen to take me on trial.
“Luckily it’s gone really well and I’m keen to repay the faith they’ve shown in me.
“Glasgow’s a club and a city that’s got a proud rugby history, both professionally and back in the amateur era.
“I always wanted to go overseas with my rugby if the opportunity came up, and Glasgow were keen to bring me over and have a look at me.
“All the boys have been great since I arrived. They’ve all really helped me out – coming in halfway through a season is always difficult but they’ve helped me fit in really well.”