The ex-Marine and US Senator had been in hospital in Columbus, Ohio, for more than a week and died surrounded by his children and wife of 73 years.
Glenn is best known for circling the earth in 1962 aboard a space capsule dubbed Friendship 7.
His achievement marked the moment the US caught up with the Soviet Union in manned space exploration.
Glenn is expected to be buried at Arlington National Cemetery, Virginia.
“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!” Ohio Governor John Kasich said in a statement
After returning to Earth, Glenn was elected in 1974 as a Democrat to the US Senate, where he served for 25 years.
But he once again defied gravity, as well as age, in 1998 – 36 years after his historic flight – when he became the oldest man to travel to space at age 77.
The only son of a plumber and schoolteacher, Glenn was born in 1921 in Cambridge, Ohio.
His father would recall how the boy used to run around the yard with arms held wide, pretending to fly a plane.
Glenn retained a lifelong love of flight and was piloting his own aircraft as recently as five years ago.
He married his childhood sweetheart, Annie Castor, and they had two children, David and Lyn.
Glenn’s wife retains the $125 diamond engagement ring he bought for her in 1942.
He became a combat pilot, serving in World War II and the Korean War before joining America’s space agency.
Glenn earned six Distinguished Flying Crosses and flew more than 150 missions during the two conflicts.
After setting the transcontinental flight speed record as a test pilot, he joined Mercury 7, America’s first class of astronauts.
On 20 February 1962, he blasted off solo from Cape Canaveral aboard a cramped capsule on an Atlas rocket to a new frontier for Americans.
He spent just under five hours in space, completing three laps of the world.
“Zero G (gravity) and I feel fine,” was Glenn’s remark on weightlessness.
His capsule’s heat shield came loose, leading Mission Control to fear he would burn up during re-entry, but the craft remained intact.
After splashdown in the Atlantic, Glenn was treated to a New York ticker-tape parade.
During his political career he was briefly considered as a running mate for Democratic presidential candidate Jimmy Carter.
But Glenn’s star dimmed after a meandering keynote address at the 1976 Democratic National Convention that led Mr Carter to call him “the most boring man I ever met”.
He vied himself to be the party’s White House standard-bearer in 1984, but was beaten by Mr Carter’s Vice President, Walter Mondale.
Glenn’s business career, which included an investment in a chain of Holiday Inns, made him a multi-millionaire.
When he returned to space in 1998, despite the misgivings of his wife, he said in a news conference from orbit: “To look out at this kind of creation out here and not believe in God is to me impossible.”
In 2011, Glenn received the Congressional Gold Medal, the nation’s highest civilian award.
A year later, President Barack Obama presented him with the Presidential Medal of Freedom.
Mr Obama said in a statement on Thursday that Glenn had “spent his life breaking barriers”.
Nasa tweeted that he was “a true American hero”.
“Godspeed, John Glenn. Ad astra”, it added, a Latin phrase that means, “to the stars”.
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