Brady, who spent much of the rest of his life in a wheelchair, died at a retirement community in suburban Alexandria, Virginia, where he lived with his wife.
"We are heartbroken to share the news that our beloved Jim 'Bear' Brady has passed away after a series of health issues," Brady's family said in a statement. "His wife, Sarah; son, Scott, and daughter, Missy, are so thankful to have had the opportunity to say their farewells."
Former first lady Nancy Reagan said she was "deeply saddened to learn of Jim Brady's passing today. Thinking of him brings back so many memories happy and sad of a time in all of our lives when we learned what it means to 'play the hand we're dealt.'"
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President Barack Obama described Brady as a White House legend, who turned "the events of that terrible afternoon into a remarkable legacy of service."
Thanks to Brady and the law bearing his name, "an untold number of people are alive today who otherwise wouldn't be," the president said in a statement.
Josh Earnest, Obama's press secretary, said Brady "showed his patriotism and commitment to the country by being very outspoken on an issue that was important to him and that he felt very strongly about."
A news clip of the shooting, replayed often on television, showed Brady sprawled on the ground as Secret Service agents hustled the wounded president into his limousine.