"We are heartbroken to share the news that Neil Armstrong has passed away following complications resulting from cardiovascular procedures," his family said in a statement. "Neil was our loving husband, father, grandfather, brother and friend."
Armstrong had heart surgery several weeks ago. His family did not say where he died.
Armstrong commanded the Apollo 11 spacecraft that landed on the moon July 20, 1969. Half a billion people watched a black-and-white TV image as he backed down the ladder of the lunar landing ship, planted his left foot on the moon's surface, and said, "That's one small step for a man, one giant leap for mankind."NASA footage - See Neil Armstrong take first steps on the moon
Twenty minutes later his crewmate, Buzz Aldrin, joined him, and the world watched as the men spent the next two hours bounding around in the moon's light gravity, taking rock samples, setting up experiments, and taking now-iconic photographs.
"Whenever I look at the moon it reminds me of the moment over four decades ago when I realized that even though we were farther away from earth than two humans had ever been, we were not alone," Aldrin said in a statement. "Virtually the entire world took that memorable journey with us. I know I am joined by millions of others in mourning the passing of a true American hero and the best pilot I ever knew."
The moonwalk marked America's victory in the heated Cold War space race that began Oct. 4, 1957, with the launch of the Soviet Union's Sputnik 1, a 184-pound satellite that sent shock waves around the world.Read national reactions to Neil Armstrong's death
"Neil was among the greatest of American heroes - not just of his time, but of all time," President Barack Obama said in a statement. "When he and his fellow crew members lifted off aboard Apollo 11 in 1969, they carried with them the aspirations of an entire nation. They set out to show the world that the American spirit can see beyond what seems unimaginable - that with enough drive and ingenuity, anything is possible. And when Neil stepped foot on the surface of the moon for the first time, he delivered a moment of human achievement that will never be forgotten."
Armstrong never allowed himself to be caught up in the celebrity and glamour of the space program, despite his recognition around the world.
"I am, and ever will be, a white socks, pocket protector, nerdy engineer," he said in February 2000 in one of his rare public appearances. "And I take a substantial amount of pride in the accomplishments of my profession."
Armstrong was a native of the small town of Wapakoneta, Ohio. He was married to the former Jan Shearon and living near Edwards Air Force Base in the high desert of California.
ABC News and the Associated Press contributed to this report.