Schmidt has held several roles within Google. He was Google's CEO in 2001 and then became executive chairman in 2011 when co-founder Larry Page took over the role of CEO. He stayed as executive chairman after the Alphabet restructuring.

"Larry, Sergey, Sundar and I all believe that the time is right in Alphabet's evolution for this transition. The Alphabet structure is working well, and Google and the Other Bets are thriving," said Schmidt in a statement.

Alphabet expects to appoint a non-executive chairman in the near future.