The uncapped 27-year-old moves on after five years at Scotstoun having made 46 appearances to date for his hometown club.
First called into the Scotland squad ahead of the subsequently-cancelled 2021 summer tour, the former Glasgow Accie was added to Gregor Townsend’s pool earlier this week ahead of the Six Nations clash with France.
"I have loved the last five years playing for Glasgow,” McDonald said. “For a local lad, it means a lot to play for your home team and very few get to do that, so to represent the city of Glasgow has been an honour and a privilege.
"I've made some friends for life at this club and always thank Glasgow Warriors for the opportunities I’ve had to pull on the jersey.”
Head coach Danny Wilson added: “We’re obviously disappointed to see Kiran leave the club, but when he does, we will wish him well.
"This season he’s played well for us and has earnt his call up to the national squad.
"When he returns to us from Scotland duty, I’m sure he’ll be as determined as ever to end his time here on a high.”
Wasps head coach Lee Blackett was thrilled to add the 6ft 8in forward ahead of next season.
“We have been following his progress for the last couple of years and Kiran is currently enjoying his best season so far at Glasgow.
“Kiran is a great athlete with a lot of potential, he has the ability to play at six or second row, that flexibility will be vital for us over the course of next season.”