The longtime executive will transition to becoming a technical advisor at the company's regular board meeting in January.
"Since 2001, Eric has provided us with business and engineering expertise and a clear vision about the future of technology", said Larry Page, Alphabet's CEO and Google's co-founder. On his next journey as technical advisor Schmidt said, "The time is right in Alphabet's evolution for this transition".
CNBC reports that Schmidt's new role will likely include advising "the company's urban development arm, Sidewalk Labs, its deep learning efforts, and its healthcare spin-offs, Verily and Calico".
As chief executive, Schmidt steered Google through its 2004 initial public offering.
Schmidt was hired as the company's first outside CEO in 2001, having previously served as CEO of Novell, a now-defunct Utah-based software company.More news: At least four Indian soldiers killed in Kashmir border firing
Alphabet owns Google Search, Maps, Ads, Gmail, Android, Chrome and Youtube and has more than 70,000 employees. Schmidt joked when he stepped down in 2011 that "day-to-day adult supervision no longer needed!"
Page became chief executive at Alphabet, a holding company for the tech giant's search products and "other bets" such Waymo self-driving vehicle unit; Nest smart home gadgets, and Google Fiber internet service. He steps down with the company firmly in place as the undisputed leader in search and online advertising worldwide.
Other companies in the lawsuit which reached earlier settlements included eBay, Lucasfilm, Pixar and Intuit.
Alphabet shares ended Thursday 0.25% lower at $1,070.85.
Schmidt was listed as a donor and advisor to the winning campaign by Barack Obama to become U.S. president in 2008. In recent years, Schmidt has taken to philanthropy. Alphabet also said in a statement that, "The company anticipates that the Board will appoint a non-executive chairman".