Ternus, the current head of hardware engineering who has been at Apple for 25 years, will take over on 1 September and Cook will become executive chairman. BBC reported.
Cook has been chief executive of Apple since 2011 after co-founder Steve Jobs resigned for health reasons, shortly before his death.
Cook will stay as chief executive through the summer to work with Ternus on the transition after which he will "assist with certain aspects of the company, including engaging with policymakers around the world".
Cook's decision to step away from the chief executive role follows months of speculation that Apple - which has just celebrated its 50th anniversary - was looking for a successor.
