"We now have a person at the top of the Republican ticket who I believe is dangerous, doesn't understand the complex world we live in, doesn't care to, and is without any moral or international philosophy," Gregg said in a statement on Sunday.
"I've met Hillary Clinton a number of times and followed her career in public service. I'm impressed with her knowledge and experience. She would make an extremely good president."
Gregg, 88, served as Bush's national security adviser from 1982 to 1989 and was part of late President Reagan's administration for eight years. He was ambassador to South Korea from 1989 to 1993.
George H.W. Bush was also voting for Clinton, it was revealed last week by Kathleen Hartington Kennedy Townsend, the former Maryland lieutenant governor and daughter of the late Robert F. Kennedy.
Bush's national security advisor during his presidency, Brent Scowcroft (1989-1993), has also endorsed Clinton.
