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.
Jamie Carragher: Arsenal And Liverpool 'Will Always Fall Short' Of Winning Trophies
In August, Liverpool had all but annihilated Arsenal with their blitzkrieg and a similar story unfolded in the first half. "This is another draw we should have won and that's a very important thing because it's a development", Klopp said.
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.
Mourinho Opens Up On Leicester Clash, Bristol City Shock, Valencia, Fellaini Injuries
United manager Jose Mourinho made 10 changes from the side that beat West Brom last weekend, with only Marcus Rashford retained. Nonetheless, they have not kept a clean sheet away from Old Trafford since October so Leicester could profit from that.
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.
Four members of the Minnesota Vikings voted to this season's Pro Bowl
He is the first Vikings cornerback selected to two straight Pro Bowls since Antoine Winfield made it three straight from 2008-10. The Packers also released fullback Joe Kerridge from the active roster and quarterback Jerod Evans from the practice squad.
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.