The internet firm said Schmidt would focus on "deals, partnerships, customers and broader business relationships", while Page would lead product development and technology strategy.
Google's other co-founder, Sergey Brin, is to focus on strategic projects and new products.
The news came as Google posted strong net profits in the past quarter of $2.54bn (£1.6bn) on revenues of $8.44bn. Net revenues were $6.37bn, about $300m more than analysts had forecast.
Page is returning to the role he gave up to Schmidt a decade ago when investors demanded a more experienced business leader.
Schmidt said the changes were part of a plan to speed up decision making and simplify the management structure at Google.
He denied the changes were prompted by any particular competitive threat, according to the Financial Times.
Shares of Google rose about 2% to $639 in after-hours trading on Wall Street.
The company now has a market value of about $200bn and has turned the co-founders and Schmidt into billionaires, the BBC reported.
This story was first published by Computer Weekly