Glenn died at James Cancer Hospital in Columbus, Ohio, where he was hospitalized for more than a week, according to the John Glenn School of Public Affairs.
He was the third U.S. astronaut in space, and became an American hero when he became the first to get into orbit back in 1962.
"Godspeed, John Glenn," fellow astronaut Scott Carpenter radioed just before Glenn blasted off from Cape Canaveral.
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"Zero-G and I feel fine," Glenn famously quipped as he orbited Earth three times during his mission.
He served his native state of Ohio as a Democrat in the U.S. Senate for 24 years, longer than any other state senator in Ohio's history, and briefly ran for president in 1984.
Glenn would return to space at the age of 77 aboard the space shuttle Discovery in 1998. He still holds the record for the oldest person in space.
"To look out at this kind of creation out here and not believe in God is to me impossible," Glenn said while aboard Discovery.
In 1957, Glenn broke the transcontinental airspeed record, flying from Los Angeles to New York City in three hours, 23 minutes and 8 seconds.
Before dangerous space missions and breaking aviation records, Glenn flew 149 combat missions as a fighter pilot in World War II and the Korean War.
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"The last of America's first astronauts has left us, but propelled by their example we know that our future here on Earth compels us to keep reaching for the heavens. On behalf of a grateful nation, Godspeed, John Glenn," President Barack Obama said in part of a written statement released following Glenn's death.
"Today we lost a great pioneer of air and space in John Glenn. He was a hero and inspired generations of future explorers. He will be missed," President-elect Donald Trump wrote on Twitter.
Today we lost a great pioneer of air and space in John Glenn. He was a hero and inspired generations of future explorers. He will be missed.— Donald J. Trump (@realDonaldTrump) December 8, 2016
"John Glenn is, and always will be, Ohio's ultimate hometown hero, and his passing today is an occasion for all of us to grieve," Ohio Gov. John Kasich wrote in part of a statement released following Glenn's death. "Though he soared deep into space and to the heights of Capitol Hill, his heart never strayed from his steadfast Ohio roots. Godspeed, John Glenn!"
Glenn's body will lie at the Ohio Statehouse for a day and a public memorial service will be held at Ohio State University's Mershon Auditorium, according to ABC News. He will be buried at Arlington National Cemetery in a private service.
The Associated Press contributed to this report.