Google co-founders Larry Page and Sergey Brin, Google Chief Executive Sundar Pichai "and I all believe that the time is right in Alphabet's evolution for this transition", Mr. Schmidt said in the statement.
"In recent years, I've been spending a lot of my time on science and technology issues, and philanthropy, and I plan to expand that work", Mr Schmidt added. In 2015, Google restructured to become Alphabet and Schmidt assumed the same role at the newly named parent company.
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The company says it expects to "appoint a non-executive chairman", presumably sometime next year.
Schmidt has been a key figure at Google for some 17 years.
Alphabet owns Google Search, Maps, Ads, Gmail, Android, Chrome and Youtube and has more than 70,000 employees.
During his tenure, Schmidt wound up at the center of a civil suit in USA federal court over an "anti-poaching" agreement involving tech giants Apple, Google, Intel and Adobe.
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The group also owns the Other Bets unit, which includes the Waymo driverless vehicle business and the Project Loon WiFi-enabled weather balloon venture.
Other companies in the lawsuit which reached earlier settlements included eBay, Lucasfilm, Pixar and Intuit.
Forbes, which ranked Schmidt at No. 119 on its list of the world's billionaires, calculates that the outgoing chairman has net worth of $11.1 billion.
Alphabet shares ended Thursday 0.25% lower at $1,070.85. He was a member of President Barack Obama's Council of Advisors on Science and Technology, and helped the government fix the health care website after a disastrous rollout.
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Orrin Hatch of Utah, House Minority Leader Nancy Pelosi of California, and three former USA attorneys general. The Obama administration rebuffed arguments in favor of Rubashkin, and in January, Chief U.S.
Schmidt is also known to speak out on technology issues, expressing concerns about matters such as online spying and barriers to the free-flow of data.