"I am enormously proud of my last decade as CEO, and I am certain that the next 10 years under Larry will be even better!" wrote Schmidt in a post on Google's official blog. "Larry, in my clear opinion, is ready to lead."
Page will take over April 4, with Schmidt taking the title of executive chairman, in which, Schmidt said, he will focus on building relationships with customers, business partners and the government.
Page, who founded Google in 1998 with fellow Stanford University graduate student Sergey Brin, has long been considered the firm's thought leader, driving strategy and pushing the company into new areas as far afield as wind energy.
"Larry, Sergey and I have been talking for a long time about how best to simplify our management structure and speed up decision making - and over the holidays we decided now was the right moment to make some changes to the way we are structured," Schmidt wrote on the company blog.
Tech analysts say the changeover should not result in any major shift in strategy.
"In my book, this ranks as one of the least dramatic management changes you could have," said Mark Mahaney, a managing director of Citigroup, who has been analyzing Google since it went public in the early 2000s. It would have been more significant if Google had "seen an external CEO come in, or see that Eric was retiring or going to another company."
The news came as the Mountain View, Calif.-based company reported a $2.54 billion profit in the fourth quarter of 2010, up nearly 29 percent from the comparable period a year earlier. It's also just days after another management shake-up in the tech world, with Apple chief executive Steve Jobs announcing that he would be taking another medical leave of absence.
By many accounts, Google has been run for years as a fairly harmonious triumvirate: Schmidt, Page and Brin. Schmidt, a seasoned Silicon Valley executive, was brought on board in 2001 to help the search firm harness its explosive growth.
Ken Auletta, the New Yorker magazine writer who visited the company's campus over two years while writing his 2009 book "Googled: The End of the World As We Know It," said the troika's easy relationship rarely was tense, even when there were disagreements over significant issues.
When Google was considering pulling out of China over government censorship, Schmidt had argued to stay, but Page and Brin had decided it was better to leave. "Eric was confident enough to admit, 'I disagree with them, but it's their company.' He always acted as if it was their company," Auletta said.
When Schmidt came on board, there was some division between him and Page and Brin, but only briefly, Auletta said. Schmidt seemed strange to them. The CEO was a generation older, wore suits and drove a Mercedes. The young founders did not. So, Bill Campbell, a senior executive, was brought in as the management team's "coach" and, eventually, relations smoothed. A genuine partnership, with respectful and jocular back and forths, was built.
"Eric would make fun of them in a warm way, not in a disdainful way," Auletta said. "If he went around the room saying he was the grown-up, they were not insulted."
But Page always wanted to run the company, Auletta said. He read books on management when he was younger and prided himself on his leadership style. Page also wanted to avoid what happened to Serbian Nikola Tesla, an early- 20th-century pioneer in electricity who was terrible with money.
"One of the reasons Larry would say 'I want to run my own company' is because of Tesla," Auletta said. "Tesla didn't run his own company and gave away his inventions."
Auletta said Schmidt was probably "nudged" or "jumped on his own," and not pushed. "I could see him joining the Obama administration. He loved being out there as one of Obama's economic advisers. He loved jumping on his private plane and flying around."
"Day-to-day adult supervision no longer needed!" wrote Schmidt on his Twitter account shortly after the company made the announcement Thursday.
Google continues to churn out steady profits from the sale of ads that appear alongside its search engine results. Yet the firm will have to navigate challenges as it builds on its dominance.
Last year Facebook, the world's largest social-networking site, surpassed Google to become the most popular site on the Web, according to two research firms. Meanwhile, Google has struggled to launch a successful social-networking services of its own; products such as Wave have failed to catch on.
More importantly, Facebook's trove of data is beyond the reach of Google's search algorithms, which is troubling for a company whose goal is to make people turn to its products - and stay on them - as much as possible.
Google is trying to grow by acquiring a wide spread of tech firms, which has triggered the scrutiny of antitrust regulators who are scrubbing the company's every move for signs that it is abusing its dominance.
As Page takes over, he will also have to drive Google's expansion into the mobile phone market with its Android software, which has pitted the search firm against Apple and its iPhone platform.
"As the company has grown up, the founders have, too," said Rebecca Arbogast, a tech analyst at Stifel Nicolaus.