Joe Maddock, meanwhile, will take over as Canterbury coach next year.
Highlanders chief Roger Clark said he was chuffed to hand the club's defensive reins to Delaney after the success of McLeod's tenure, which included frequent Super Rugby finals berths and the 2015 title.
A well-travelled loose forward in his playing days, Delaney spent time with both Nottingham and London Irish before joining Canterbury.
"We were aware it might be a global search to find the right candidate - ironically, almost all of Glenn's coaching experience is offshore, but in a stroke of good fortune he landed right under our nose," Clark said.
"I'm sure all our players will benefit from Glenn's experience."
Delaney admitted he was torn between Canterbury, where he has been at the helm for just one season, and a new experience in Dunedin.
But the challenge of coaching at the Super Rugby level was too great to resist.
He was certain Maddock would do the province proud in 2018.
"I've seen first hand what an excellent coach Joe is, and just how passionate he is about this team," the 43-year-old Delaney said.