Google (NSDQ: GOOG) CEO Eric Schmidt (pictured, right) may have passed on the chance to be President Barack Obama’s chief technology officer, but he has agreed to be part of the president’s Council of Advisors on Science and Technology. Schmidt was among 20 people named to the council Monday, including Microsoft (NSDQ: MSFT) Chief Research and Strategy Officer Craig Mundie (Most of the other appointees are academics, in contrast to the Council under President George W. Bush, which was heavy with businesspeople.)

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Both Google’s Schmidt and Microsoft’s Mundie have been Obama supporters. Schmidt campaigned for Obama and served as an advisor on technology issues during the campaign, while Mundie donated $25,000 to the president’s inauguration. Schmidt also happens to be serving on a government “economic recovery committee” in Great Britain too.

Obama has said that he hopes the Council, which has existed since 1990, will be “a vigorous external advisory council that will shape my thinking on the scientific aspects of my policy priorities.” High on his technology agenda—increasing broadband penetration, establishing electronic health records and improving math and science education.