Alphabet plans to appoint a non-executive chairman to replace Schmidt.
Alphabet, which was formed when Google restructured its operations in 2015, now has more than 70,000 employees worldwide, and owns Google Search, Maps, Ads, Gmail, Android, Chrome, and YouTube.
Alphabet's "Other Bets" businesses include self-driving vehicle company Waymo, and other technology companies such as Nest, Fiber and Verily. He served as the company's CEO from August of that year through April 2011, when he became executive chairman of the board of directors at Google.
"Larry, Sergey, Sundar and I all believe that the time is right in Alphabet's evolution for this transition", Schmidt said in a statement, referring to Alphabet's co-founders Larry Page and Sergey Brin and Google's current chief executive Sundar Pichai.
Schmidt said in a statement that he felt the Alphabet structure was working well, with Google and its other bets thriving. Schmidt joked when he stepped down in 2011 that "day-to-day adult supervision no longer needed!". The business will join Apple and Microsoft who are both huge companies with a non-executive chairman.
Other companies in the lawsuit which reached earlier settlements included eBay, Lucasfilm, Pixar and Intuit.
In 2001, Google brought Eric Schmidt on board as CEO.
Schmidt ranks among the world's richest people.
GOOGL closed Thursday's trading session 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.
His philanthropic endeavors include the Schmidt Family Foundation established with his wife and focus on challenges such as climate change and protecting the environment.