The first time Tim Cook interviewed Angela Ahrendts they met in Cupertino, Calif., where Apple is based, but not at Apple’s offices. An Indiana native, Ahrendts was CEO of Burberry in London at the time, and Cook was looking for a new head of Apple’s retail operation, his previous hire not having worked out. Both were famous, and least in certain circles, and the two didn’t want to be spotted together.

Ahrendts had been thriving at Burberry, and was flattered to be called but hardly thought she’d join Apple. “I did not expect to be moved by the man, and I left and I thought, “Ohhhhh! My life was perfect. Aaargh, why, why, why?”

A leader is expected to wear many hats. Recruiter of talent is one of them. Cook clearly succeeded with Ahrendts, who spoke to Fortune for an article about her boss’s leadership qualities. “The first time I sat down with him, I walked away thinking wow, that’s a man of peace,” she says. “I just absolutely loved his integrity, his values. Nothing anybody can write, say, or do is going to take him off of always doing the right thing. Not just for Apple, but for Apple’s people, for communities, for countries. The world needs more leaders like Tim.”

As a newcomer who was a longtime admirer of Apple AAPL under Steve Jobs, Ahrendts brings a unique perspective to the Cook era among Apple’s senior management team. “Steve’s whole raison d’être just enriched and changed people’s lives,” she says. “Then Tim’s added a whole other level, which is: Apple has gotten so big that it is our responsibility to leave it better than we found it.”

Cook and Ahrendts spent their initial time getting to know one another rather than going deep on strategy or fashion. “We talked about the future of retail, about where is retail going and what is Apple’s role in that. We talked much more about the future. We didn’t talk a lot about fashion.”

Ahrendts has been at Apple for almost a year and hasn’t yet revealed any big changes she plans for its stores. As a result, she has at least temporarily lowered what was a very high profile she maintained at Burberry. To hear Cook tell it, though, she isn’t having any trouble getting used to Apple, or vice versa. “Angela and I talked over a long period of time, although I knew instantly when I met her that I wanted to work with her,” he says. “She’s a perfect culture fit. Within a week, it felt like she’d been there a year. And now it feels like she’s been there multiple years. When you start to finish each other’s sentences, this is a good thing.”

Leadership, after all, is about nurturing and promoting talent. And talking them up too.