While Schmidt left the role of CEO, he has been acting as the company's executive chair ever since - and took on the same role at Alphabet, formed in 2015 to act as a parent company for Google and associated ventures.
"Larry, Sergey, Sundar and I all believe that the time is right in Alphabet's evolution for this transition", said Schmidt in a statement, referring to Google cofounder Sergey Brin and CEO Sundar Pichai.
Google is hoping that Schmidt's move should enable him to bring the same focus and energy he brought to Google to his other interests, while continuing to advise Alphabet. Schmidt also plans to devote more time to philanthropy. He helped take Google public in 2004 and built it into a colossus. Page had previously worked at Sun Microsystems and Novell before being hired by Page and Brin in 2011 to run the company.
Schmidt also had a seat on Apple's board of directors from August 2006 until three years later when Google's ambitions for Android became problematic for Apple.
Page, in a statement Thursday, alluded to the new generation at Alphabet and Google. "I'm incredibly excited about the progress our companies are making, and about the strong leaders who are driving that innovation".
Eric Schmidt has always been a major figure in Google and even when the company transitioned to Alphabet.
The group also owns the Other Bets unit, which includes the Waymo driverless auto business and the Project Loon WiFi-enabled weather balloon venture.
The key outlet for that philanthropy has been The Schmidt Family Foundation, founded by Schmidt and his wife Wendy in 2006.
Meanwhile, Alphabet is expected to appoint a new chairman at a meeting next month.
Mr Schmidt first joined Google as CEO back in 2001 when the company only had several hundred employees.