The family said Armstrong died following complications from cardiovascular procedures, CBS News reported.
The family said besides being a loving family man, Armstrong was "a reluctant American hero who always believed he was just doing his job."
Armstrong commanded the Apollo 11 mission that landed on the moon on July 20, 1969. As he stepped onto the lunar surface, he radioed back to Earth, "That's one small step for a man, one giant leap for mankind." He later insisted he said "small step for a man" but the "a" was lost in transmission.
NBC said Armstrong and his wife Carol married in 1999, and lived in the Cincinnati suburb of Indian Hill. Armstrong largely stayed out of public view.
Armstrong had just celebrated his 82nd birthday when a stress test earlier this month in a Cincinnati area hospital revealed problems, and surgeons performed a quadruple bypass.
Fellow Apollo astronaut Gene Cernan told NBC News Armstrong's wife told him her husband's spirits were high and doctors were confident there would be no problems with recovery.
Armstrong was a reluctant, unassuming space hero whose "one small step" reverberated around the world.
Back on earth 238,000 miles away, millions of people watched the ghostly images and listened through an elaborately engineered live television system. Most would agree it was a stunning moment, one that to many was the fulfillment of an ages-long dream, one that turned science fiction into scientific fact. It also was the fulfillment of President John F. Kennedy's 1961 vow to put a man on the moon by the end of the decade.
Armstrong and his Apollo XI co-pilot, Edwin "Buzz" Aldrin, the second man to step on the moon, spent about two and one-half hours walking on the moon collecting samples, doing experiments, and taking photographs. They set up a passive seismograph experiment and a laser ranging retro-reflector. They collected 46 pounds of lunar rocks, judged to be 3.7 billion years old.
When Armstrong returned to Earth, he was hailed a hero, decorated by 17 countries and given dozens of medals and honors. Only 38 years old at the time, he was admired by many people who marveled at his ability and poise under pressure.
But Armstrong, basically a very private man, thought the adulation was overdone; "disproportionate," he told writer Andrew Chaiken, author of 1994's "A Man on the Moon." In his mind, he said, the landing itself was the flight's most significant accomplishment, one he and Aldrin achieved at the same instant.
NASA sent Armstrong and Aldrin throughout the world to promote their out-of-this-world adventure. Together with Michael Collins, the third man on their voyage, they gave a first hand look at the flight in the 1970 book "First on the Moon."
Afterward, though not reclusive, Armstrong attended few public events. But, when possible, he spent time at his remote dairy farm in Lebanon, Ohio, about 100 miles from Wapakoneta, his birthplace.
Armstrong, who earned his first pilot's license before he could legally drive a car, was chosen in1962 for the new U.S. Astronaut program. He had a glowing resume by that time as a Navy fighter pilot -- he flew 78 combat missions in the Korean war -- and as a NASA test pilot in the 1950s.
His test pilot days peaked when he took the prestigious X-15 to the fringes of space at an altitude of over 200,000 feet and 4000 miles per hour. During those days he flew more than 200 different models of aircraft, including jets, rockets, helicopters and gliders.
He also took a turn as an aeronautical research scientist and earned a masters degree in aerospace engineering from the University of Southern California. Eventually, he collected honorary doctorates from a number of universities.
As an astronaut, Armstrong served as backup pilot on the Gemini V flight and as command pilot on the 1966 Gemini VIII flight which performed the first successful docking of two spacecraft. He subsequently flew on the Gemini VIII mission before his epochal Apollo XI flight.
"I believed that a successful lunar landing could, might, inspire men around the world to believe that impossible goals were possible, that the hope for solutions to humanity's problems was not a joke," he said.
Neil Alden Armstrong was born on Aug. 5, 1930, on his grandparents' farm near Wapakoneta, to Stephen and Viola Armstrong. He was the youngest of three children. His father was a state auditor and for a time that meant a lot of travel for Armstrong clan.
Young Neil developed an interest in flying when he was only 2 after his father took him to the National Air Races in Cleveland. His interest intensified when, at 6, he went for his first airplane ride in a Ford Tri-Motor.
From then on, he claimed an intense fascination with aviation. As a boy, he read avidly from airplane magazines and made copious notes. His room was decorated with the many model planes he made from whatever material he could find.
Armstrong began flying lessons when he was 15 and had his student pilot's license a year later, before he got his driver's license and before he graduated from high school in 1947. A Navy scholarship got him into Purdue where he began studying aeronautical engineering. The Korean conflict interrupted his studies when the Navy called him up and made him an aviator.
He and his wife, Janet, whom he married in 1956, had two sons, Eric and Mark. They divorced in 1994.
He downplayed his own achievements as an astronaut, to the dismay of some but, author Chaikin, in his book on Armstrong and his fellow space pioneers, said it was the way to go.
"Armstrong has handled the demands of his fame by rationing himself," he said. "While some of his colleagues, and others at NASA, wish he were a more visible spokesman for the agency and for the cause of space exploration, most of the others praise his approach. They say Armstrong was the ideal 'choice' for the role of first man on the moon, as if it were an office to be filled. Were he more visible, they say, he would cheapen its currency."
As Armstrong once told a National Press Club audience: "I am, and ever will be, a white socks, pocket protector nerdy engineer. And I take a substantial amount of pride in the accomplishments of my profession."
The way he saw it: "Science is about what is; engineering is about what can be."
Armstrong subsequently held the position of NASA's deputy associate administrator for aeronautics in the early 1970s. In that position, he was responsible for the coordination and management of overall NASA research and technology work related to aeronautics.
After resigning from NASA in 1971, he became a professor of Aerospace Engineering at the University of Cincinnati from 1971 to 1979. During the years 1982-1992, Armstrong served as chairman of Computing Technologies for Aviation, Inc., in Charlottesville, Va. He then became chairman of the board of AIL Systems, Inc., an electronics systems company in Deer Park, New York.
Other endeavors included a stint as a spokesman for Chrysler, host of a cable TV documentary series on the history of flight and aided historians researching Apollo.
In 1986, Armstrong served as vice chairman of the presidential commission investigating the Challenger disaster,
Armstrong received the Medal of Freedom, the highest award offered to a U.S. civilian. Armstrong's other awards coming in the wake of the Apollo 11 mission included the NASA Distinguished Service Medal, the NASA Exceptional Service Medal, seventeen medals from other countries, and the Congressional Space Medal of Honor.