They will leave their respective roles as Alphabet’s chief executive officer and president but remain on the board.
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”.
But in a blog post on Tuesday, the co-founders, both aged 46, 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 said it was the “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,” their letter said.
They declared it was time to “assume the role of proud parents, offering advice and love, but not daily nagging”.
The 47-year-old was born in India, where he studied engineering. He went on to study in the US at Stanford University and the University of Pennsylvania before joining Google in 2004.
“The founders have given all of us an incredible chance to have an impact on the world,” Mr Pichai said. “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.”