Ternus, who joined Apple in 2001, has recently overseen the company's hardware engineering efforts and has played a key role in reigniting sales of products such as Apple's Mac computers, which have gained market share in recent years.
Cook, who has led Apple since 2011, will become the company's executive chairman, the company said in a statement on Monday.
At 50, Ternus is the same age Cook was when he took over CEO duties from Apple co-founder Steve Jobs. He most recently showed the company's iPhone Air last autumn, the biggest revamp of the iPhone since 2017 and a key proving ground for several new chips.
Ternus, who helped bring about now-ubiquitous products such as iPads and AirPods, will be tasked with helping Apple navigate a technology landscape upended by AI, after losing its crown as the world's most valuable company to Nvidia.
Ternus will have to fend off Nvidia, which has announced its own personal computer and is working on chips that can power laptops, as well as rivals such as Meta Platforms, whose augmented-reality glasses have become a surprise hit with just a fraction of the capabilities - and price tag - of Apple's Vision Pro headset.
"The promotion of Mr. Ternus indicates the company will focus on new hardware devices such as folding phones, glasses, VR devices and AI pins," said Gil Luria, managing director of D.A. Davidson & Co.
Cook, who presented a custom golden plaque to US President Donald Trump, would also continue to engage with policymakers, the company said.
In naming Ternus chief executive, Apple is shifting from a supply-chain guru who helped turn Apple into a global brand that churns out hundreds of millions of units per year, to a leader who has long focused on design and products.
Ben Bajarin, CEO of technology consulting firm Creative Strategies, said Ternus is well-liked within Apple "and will bring fresh energy."
Separately, Apple said that Johny Srouji, who has overseen Apple's custom chip and sensor designs, has been named chief hardware officer.
