Apple did not respond to a request for comment.
Schmidt's departure had been expected by many analysts as Apple and Google began to increasingly compete against each other in areas such as smartphones and computer operating systems.
According to corporate governance guidelines posted on Apple's Web site, the company's directors meet at least four times a year.
Apple's board currently has seven members, of which only one, Chief Executive Steve Jobs, is an officer of the company.
Some analysts believe the company may move to name Chief Operating Officer Tim Cook to the board. Cook oversaw day-to-day operations for Apple while Jobs was on medical leave.
The other Apple board members are J. Crew CEO Millard Drexler, Intuit Chairman Bill Campbell, Harwinton Capital CEO Jerry York, Avon Products CEO Andrea Jung, former Genentech CEO Arthur Levinson and Former Vice President Al Gore.
(Reporting by Gabriel Madway)