His family said in a statement that Brady, 73, had a "series of health issues."
"Over the years, Jim inspired so many people as he turned adversity into accomplishment," the family said.
John Hinckley Jr., a young man obsessed with the actress Jodie Foster and the Taxi Driver character Travis Bickle, opened fire on Reagan on March 31, 1981, as the president walked back to the White House from a lunchtime speech at the nearby Washington Hilton. The president and three other people were wounded with Brady so seriously injured initial reports said he had died.
Brady was permanently disabled with his wounds leaving him paralyzed on the left side.
Hinckley was found not guilty by reason of insanity. He remains at St. Elizabeth's Hospital in Washington.
After the shooting, Brady and his wife, Sarah, led what became known as the Brady Campaign to Prevent Gun Violence. The bill requiring federal background checks for gun buyers, the Brady Handgun Violence Prevention Act, was named in his honor.
Brady was born in Centralia, Ill., and graduated from the University of Illinois. He joined the Reagan campaign in 1980 after serving as a spokesman for one of Reagan's Republican rivals, former Texas Gov. John Connally, and was named press secretary in the new administration.
While Brady's active tenure in the White House was short, Josh Earnest, President Obama's press secretary, said he "really revolutionized this job." Brady, a rotund talkative man, was nicknamed "The Bear" by White House reporters.
The White House press room was named after Brady in 2000.