"We are heartbroken to share the news that Neil Armstrong has passed away following complications resulting from cardiovascular procedures," Armstrong's family said in a statement obtained by CNN affiliate WKRC.
Armstrong underwent heart surgery this month.
"While we mourn the loss of a very good man, we also celebrate his remarkable life and hope that it serves as an example to young people around the world to work hard to make their dreams come true, to be willing to explore and push the limits, and to selflessly serve a cause greater than themselves," his family said.
"For those who may ask what they can do to honor Neil, we have a simple request. Honor his example of service, accomplishment and modesty, and the next time you walk outside on a clear night and see the moon smiling down at you, think of Neil Armstrong and give him a wink."
Many Americans and even the history books omit how Armstrong earned his wings saving the Gemini 8 crew some three years earlier. After the first successful docking of a spacecraft in orbit, the Gemini 8 capsule nearly met with disaster.
As Gemini 8 tumbled wildly at 17,500 miles per hour, Armstrong decided the problem had to be a stuck thruster. He and Scott shut off each of the spacecraft's 16 orbital maneuvering system thrusters one at a time. Thruster Number 8 did not respond.
"All we've got left is the reentry control system," Armstrong told Scott. Armstrong believed those thrusters, more powerful than standard thrusters because they positioned the spacecraft for reentry, would override the stuck thruster.
"Press on," Scott said.
Both astronauts wavered on the edge of losing consciousness. At first, nothing happened. After turning the system off, then on for a second time, the reentry thrusters responded.
Armstrong guided the capsule to a water landing in the Pacific where the Navy deployed to snag the reentry vehicle. His quick thinking and cool head made him the obvious choice as mission commander when the Apollo 11 mission launched in 1969, where he became the first man on the moon.
Here's to you, Neil. Not very many people get to be the first person on another celestial body.