When she interviewed for her job at Google in 1999, Marissa Mayer was asked to list three things the fledgling search engine could do better. Reputedly, she could only think of two.

Mayer is unlikely to have the same problem when she starts her new job as chief executive of Yahoo on Tuesday. She joins a company in existential crisis, but the 37-year-old artificial intelligence star is seen as one of the few executives able to turn Yahoo around.

She joined Google in 1999 as its 20th employee – and its first female engineer – when the company was just a no-frills search page. Over 13 years at Mountain View, she has become a much-admired figure in the technology world.

"It's pretty hard to overstate her impact," Google's executive chairman, Eric Schmidt, told Glamour magazine in 2009, when Mayer became possibly the magazine's first Woman of the Year from a technology company. "She built the team that designs the products we all use."

Unlike some of her former colleagues, Mayer does not have one Google product that is known as hers. Rather, she is present in all major Google services developed over the company's first transformative decade.

Eleven years ago on Thursday, Mayer was one of 15 Googlers behind the company's famous motto: Don't Be Evil. According to Steven Levy's In the Plex, published last year, Mayer was on the three-strong team who invented Google AdWords, the groundbreaking algorithm that linked advertisers' keywords to search results and helped deliver 96% of the company's $10.6bn revenues in the first quarter of last year.

According to those who have worked with her, Mayer is as confident leading a headstrong team of male engineers as she is on the front cover of an upmarket glamour magazine. Vogue profiled her 2009 wedding to the lawyer-turned-investor Zack Brogue underneath the headline "The Bride Wore Snowflakes". Inside, the magazine fawned over Mayer's love of the designers Chanel and Oscar de la Renta.

But it is the self-styled internet geek's dedication that has made her such a passionate advocate of Google's work. On 19 August 2004, when Google made US corporate history with its $1.67bn flotation, Mayer reputedly banned her team from checking the stock price throughout the day. When the temptation for some Googlers became too much, Mayer is said to have instructed anyone caught checking the company's inflating share price to buy stock for a colleague. It was a policy that focused the mind for many of the newly made paper millionaires.

"The first and lasting impression of working with Marissa is of someone incredibly smart," said Dan Crow, a former Google product manager who worked closely with her. "She loves new ideas and finding better ways to do things. She is also extremely intolerant of sloppy or poorly prepared work. She makes decisions based on data, not intuition, so you need strong data that shows your proposal is good for users."

Crow said Mayer – who has said she attends around 70 meetings a week and spends 14-hour marathon email sessions on a weekend – introduced something approaching regular office hours at Google, a company famous for its unconventional approach to working life.

Mayer's ascent inside Google continued until 2010, when she was put in charge of the company's plateauing maps and location products, including Google Places and Street View. It was a curiously sideways move for an executive who looked cut out for the top job. One year later, co-founder Larry Page was announced as the new chief executive and Mayer, who had been integral to many of the company's successes over the past decade, was not even on the company's board of directors.

Now she joins a business in existential crisis, battered by newcomers who have stolen its advertising share and sent a succession of bosses scrambling to reinvent the technology giant as a content company.

Mayer's first day at Yahoo is on Tuesday, 24 hours after handing in her notice at the company she joined as a Stanford University graduate 13 years ago. She is heavily pregnant, expecting a baby boy on 7 October, but plans to work through her maternity leave as she breathes new life into a sleeping giant in technology.