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Delaney currently holds the position of Canterbury head coach and will start with the Highlanders, on a two year contract, at the completion of the Mitre 10 Cup.
He replaces Scott McLeod, who has moved up to the All Blacks defence coaching job.
Joe Maddock will take over as Canterbury coach next year, Newshub reports.
A well-travelled loose forward in his playing days, Delaney spent time with both Nottingham and London Irish before joining Canterbury.
Highlanders chief Roger Clark welcomed the appointment, saying: "I'm sure all our players will benefit from Glenn's experience".