Schmidt will not seek re-election to the board when his term expires in June, but will continue to advise on technical matters, according to Alphabet.
"Eric has made an extraordinary contribution to Google and Alphabet as CEO, chairman, and board member," board chairman John Hennessy said in a statement.
"We are extremely grateful for his guidance and leadership over many years."
Schmidt was on the board for more than 18 years, joining in March 2001. He was chief executive of Google from the middle of that same year until March 2011.
Google founders Larry Page and Sergey Brin recruited the proven businessman and skilled software engineer as chief executive in 2001, bringing a mature hand to the helm of the then three-year-old internet search company.
Schmidt, Page and Brin were considered a power triumvirate in control of Google. Page replaced Schmidt as chief executive a decade later.