They will leave their respective roles as Alphabet's chief executive officer and president but remain on the board.
Google's CEO Sundar Pichai will become Alphabet's CEO too, a statement said.
Alphabet was created in 2015 as part of a corporate restructuring of Google, which Mr Page and Mr Brin famously founded in a California garage in 1998.
The parent company was intended to make the tech giant's activities "cleaner and more accountable" as it expanded from internet search into other areas such as self-driving cars.
The pair moved from Google to Alphabet when it was formed - saying they were making the jump to focus on starting new initiatives.
But in a blog post on Tuesday, the pair announced they were stepping back from the day-to-day management of the company.
A joint letter said they would remain "actively involved as board members, shareholders and co-founders, but it is a natural time to simplify our management structure. We've never been ones to hold on to management roles when we think there's a better way to run the company. And Alphabet and Google no longer need two CEOs and a President".
They also declared it was time to "assume the role of proud parents - offering advice and love, but not daily nagging" and insisted there was "no better person" to lead the company into the future than Pichai.
Pichai studied engineering in India and went on to study in the US at Stanford University and the University of Pennsylvania before joining Google in 2004.
He said: "The founders have given all of us an incredible chance to have an impact on the world. Thanks to them, we have a timeless mission, enduring values, and a culture of collaboration and exploration that makes it exciting to come to work every day. It's a strong foundation on which we will continue to build. Can't wait to see where we go next and look forward to continuing the journey with all of you."
'Proud parents' who aren't giving up ultimate power."
This move represents the most significant shake-up of leadership at Google since its inception, but the reality is that Pichai has been the public face of the firm for a while.
Yet while the pair are apparently relinquishing management duties, it won't mean giving up ultimate power. Between them, they control 51 percent of voting rights on Alphabet's board. This won't change. They likened their new role to being "proud parents" to the company, looking on with close interest and care.
But should they feel the need, they can override any decision Mr Pichai makes.