Can you remember the last time the appointment of a new CEO caused as much excitement and interest as the news that Googler Marissa Mayer is taking over as CEO of Yahoo!? For the last 48 hours, the news has been dissected, discussed, deliberated over and debated extensively both in the tech and business press.

There’s good reason for it – Mayer is a prominent and popular figure, taking on a once prominent and popular web company. She has been clearly side-lined over the last 18 months at Google. Yahoo! has been sidelined by its own failed execution. They seem like a good match – a CEO with something to prove, and a company with lost glories to regain.

Most importantly for the digital industry, though, this is someone from the new wave of online businesses taking over a business from the wave before. Too often we’ve seen “safe hands” CEOs from conventional manufacturing or services companies installed at the very top of digital businesses, to mediocre or damaging effect. Could we be – finally – seeing the end of the need of “adult supervision” for the online world?

There’s still a perception that digital-age businesses need people from “proper” business to come in and run them properly. The Google folks had Eric Schmidt as adult supervision. Microsoft’s CEO Steve Ballmer worked at Procter & Gamble before joining Microsoft. Mayer’s more long-lasting recent predecessor in the revolving door Yahoo! job was Carol Bartz, whose career ran through 3M and then the computer manufacturers DEC and Sun. The record of traditional business types in online businesses is far from stellar.

Google and Apple are two of the most prominent companies in the world right now, and both are run on very different lines to traditional businesses. They have both found ways to recruit, manage and organise themselves for the information age that give them strong competitive advantages over businesses whose management hierarchies are still legacies of the industrial age. Those changes are – so far – largely confined to the organisations themselves. We haven’t seen a large-scale diaspora of executives from the upper echelons of these companies bringing their ways of working and views of business to other enterprises – yet.

Mayer is the first really prominent Googler to take the move to a big company. She’s been throughly inculcated in the culture of her former employer – as one of the first 20 employees, she helped create it. Steven Levy’s excellent and illuminating book In The Plex charts the development of the company, and makes it plain that her role was far more critical and involved than the canny, charismatic self-promoter that some accounts are trying to brand her as. Her challenge is to bring some of the digital discipline and rigour she brought to Google to an organisation that has clearly lost its way. Yahoo!, once a web-centric business, has, under various administrations, slowly drifted towards the model of a traditional media business that expresses itself mainly through the web. As many media businesses that are trying to make themselves web-centric have found over the past five years or so, that’s not a happy – or a profitable – place to be. Much of Mayer’s success or failure in her new role will depend on how well she’s able to invert that idea; can she make it a web business whose focus is media?

The answer might have a huge impact on the rest of business. If she can be the first CEO to take the culture and corporate structure innovations of Google and spread them elsewhere, we might well see this as the moment that online business started to remake the rest of business in its own image.