Gilligan, a native of Cincinnati, died at his home in the city, The Cincinnati Enquirer reported.
During his four years as governor, from 1971 to 1975, Gilligan, a Democrat, supported Ohio's first individual income tax. He successfully lobbied voters in a referendum on the tax but lost the 1974 gubernatorial election to former Gov. James Rhodes.
Before running for governor, Gilligan served several terms on the Cincinnati city council and one term in Congress. He also ran unsuccessfully for the U.S. Senate.
Gilligan served as head of the U.S. Agency for International Development from 1977 to 1981 and later taught at Notre Dame and served as director of the civic issues forum at the University of Cincinnati School of Law.
He returned to elective office as a member of the Cincinnati board of education from 1999 to 2007.
"Jack Gilligan lived his life in service to his fellow Americans, especially those in his home state of Ohio and across the United States who were left out or left behind," Obama said. "During World War II, he earned a Silver Star for his bravery at Okinawa, and he never stopped serving his country -- as a congressman, where he helped enact historic legislation from the Voting Rights Act to Medicare and Medicaid, and then as governor of Ohio."
In addition to Sebelius, Gilligan is survived by three other children and his second wife, Dr. Susan Fremont.
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