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Google said the company's other co-founder, Sergey Brin, who along with Page and Schmidt has led the "triumvirate" at the helm of the Internet search titan, would be responsible for strategic projects and new products.
The management changes, which overshadowed the Mountain View, California-based company's announcement of strong fourth quarter earnings, are due to take effect on April 4.
Schmidt, 55, a former chief executive of Novell, will remain with Google as executive chairman, focusing on deals, partnerships, customers and government outreach, Google said in a statement.
He will also act as an adviser to Page, 37, who served as CEO previously, from 1998 to 2001, and Brin, also 37.
"Day-to-day adult supervision no longer needed!" Schmidt said on Twitter in a reference to when the young co-founders brought him in to run the day-to-day operations of the then-fledgling company.
Google has grown over the past decade from a startup battling other Internet search engines into a technology giant with nearly 25,000 employees and annual revenue of nearly $30 billion.
The company meanwhile reported its fourth-quarter net profit increased to $2.54 billion from $1.97 billion a year ago, while revenue rose 26 per cent to $8.44 billion.
Technology bloggers and analysts were uncertain what exactly to make of the shakeup at the company that dominates the search market but has been coming under pressure from social networking rivals such as Facebook and Twitter.
Danny Sullivan, editor-in-chief of technology blog SearchEngineLand.com, said Google was "probably overdue for a major management reorganization."
"The structures between the three have remained exactly the same over the past 10 years - which might as well be 100 years of Internet time," he said in a blog post.
"It could be that Schmidt wants a break from being the main public face of the company."
Sullivan noted that Schmidt had come in for criticism for awkward recent statements "harmful to Google's reputation" and the three top executives may have decided "it was time for a fresh public face."
John Battelle, author of "The Search," a book about Google and technology rivals, said: "Eric has been at it for a decade, a very long time to be running a company, particularly one that has very headstrong founders in key positions of power."
"I think it's fair to say that Larry Page will not be a conventional CEO - he's not been much of a public figure for the past 10 years," Battelle added on his blog, Battellemedia.com.
"It will be interesting to see if that changes, or if Page chafes at the relentless public demands of running a massively scrutinized public company."
Venturebeat's Owen Thomas said "Page's emphasis has always been on the company’s products."
"With his ascendancy, the company's engineers will reign unchallenged - not that they had much trouble before," Thomas said.
In a blog post, Schmidt said: "Larry, Sergey and I have been talking for a long time about how best to simplify our management structure and speed up decision making."
"This triumvirate approach has real benefits in terms of shared wisdom, and we will continue to discuss the big decisions among the three of us," he added, noting each member of the trio had been equally involved in decision-making over the past 10 years.
"But we have also agreed to clarify our individual roles so there's clear responsibility and accountability at the top of the company."
He said Page was "ready to lead," and anticipated working "for a long time to come" with Page and Brin.
Page praised Schmidt as a "tremendous leader" who did an "outstanding job" leading Google.
"There is no other CEO in the world that could have kept such headstrong founders so deeply involved and still run the business so brilliantly," he added.
Google shares were up 1.35 per cent to $635.26 in after-hours electronic trading after the strong earnings results and management shakeup were announced.