Over the years Schmidt has helped turn Google, which was founded in 1998, into one of the largest, most successful and influential publicly traded companies in the world. His role has often been described as providing "adult supervision" at a company whose young co-founders like to do things in unconventional ways.

"Schmidt has a great track record and has really steered Google to great success," said Gartner analyst Ray Valdes.

Schmidt, who previously had been Novell CEO and Sun CTO, has been the public face of Google with his calm, relaxed demeanor, while running the company as a "triumvirate" with Page and Brin.

Some wondered if Page is up to the mammoth task of running such a large, powerful and increasingly diverse company.

"I guess the question is whether being Google CEO is the place to start your executive training. I can say with some assurance that if [Page] went to apply for the CEO job somewhere he wouldn't get it," said Allen Weiner, another Gartner analyst.