Among stewards of big luxury brands, Angela Ahrendts, the boss of Burberry, is probably the geekiest.

Her main achievement has been to make the 150-year-old British company the most technologically savvy of its peers. Burberry plans to be the first luxury company that is "fully digital end to end," she boasts.

But what can she do for Apple, which on Oct. 14th said it would poach her to run its retailing operations? Probably the opposite: Revive a sense of style at a tech firm that has lately looked a bit dowdy.

Many purveyors of luxury fret about cheapening their wares by selling them online. Of the 100 biggest luxury brands just 56 have transactional websites, according to Exane BNP Paribas, an investment bank.

Ahrendts, an American who took over Burberry in 2006, had no such hangups. Not content with flogging calfskin trench coats online, she has deployed every platform, device or bit of software she could think of to romance customers and spark collaboration among employees and suppliers.

IPad-wielding salespeople in Burberry stores can look up what customers have already bought, and suggest what might take their fancy next.

Ahrendts should add pizazz to Apple's bricks-and-mortar shops, which are the most profitable in America measured by sales per square foot. But that seems a small job for a woman who last year was the highest-paid chief executive of a company in Britain's FTSE 100 share index.

When she joins Apple next spring, she will merely be a senior vice president.

So the odds are that her brief will go well beyond managing Apple's stores. She can help it crack the Chinese market, where its iPhones are also-rans in the race against cheaper smartphones from Samsung and local manufacturers.

Burberry earns more than a third of its revenue in Asia compared with Apple's 28 percent.

A bigger job will be to ready Apple for the coming fusion of fashion and technology. The most talked-about new devices are wearable: Google's Glass smuggles a smartphone into a pair of spectacles. Samsung's Galaxy Gear squeezes some smartphone functions into a wrist­watch.

Apple is also keen to surf the wearable wave. An iWatch, which Apple may launch next year, would pull it toward Ahrendts' home turf, since it would compete with fashionable timepieces like the ones Burberry's sells.

Apple has long been something of a fashion house. Its product launches are choreographed like catwalk shows. But its glamour has faded since the death of Steve Jobs, its founder, in 2011.

His successor, Tim Cook, is striving to regain it. He recently hired Paul Deneve, the boss of Yves Saint Laurent, a French fashion house. Sir Jony Ive, Apple's design guru, now oversees the look of software as well as hardware.

Ahrendts brings another eye for beauty, and a knack for seducing consumers.

Copyright 2013 The Economist Newspaper Limited, London. All Rights Reserved. Reprinted with permission.