Schmidt first joined Google as CEO in 2001, back when the company only had several hundred employees, and became its executive chairman 10 years later, handing the CEO role over to co-founder Larry Page. He kept that chairmanship when Google restructured to become Alphabet in 2015, then announced he was stepping down from that role but staying on the board in December 2017.
"Eric has made an extraordinary contribution to Google and Alphabet as CEO, Chairman, and Board member. We are extremely grateful for his guidance and leadership over many years," said John Hennessy, chairman of Alphabet's board, in a statement.
Former Google Cloud chief Diane Greene, who has served on the board since 2012, will also not seek re-election. Former Oracle exec Thomas Kurian replaced Greene as head of its cloud business earlier this year.
Both of their terms will end in June.
The company has also added a new board member, Robin L. Washington, who joined on Apr. 25 and will be part of the Leadership and Compensation Committee. Washington is currently the CFO of biopharmaceutical company Gilead Sciences. Alphabet has been making an increased push into health tech, hiring David Feinberg to lead a new Google Health division last November.