Eric Schmidt, who has been with the tech giant since 2001, will remain on the board as a technical adviser on science and technology issues.
Mr Schmidt said in recent years he had spent a lot of his time on science and technology issues and philanthropy and he would expand that work.
Alphabet said it expected to appoint a non-executive chairman.
In a statement Mr Schmidt said “the time is right in Alphabet’s evolution for this transition”.
Google was founded in 1998 by Larry Page and Sergey Brin.
Mr Schmidt joined the company as chief executive in 2001, becoming chairman in 2011.
In 2015 Google restructured and the new parent company was called Alphabet with Mr Schmidt becoming chairman.
Alphabet has more than 70,000 employees worldwide, and owns Google Search, Maps, Ads, Gmail, Android, Chrome, and YouTube.
Mr Schmidt said the Alphabet structure was “working well”, and Google and other parts of the group were “thriving”.
