Brady, who served in three Republican administrations, became an advocate for stricter gun control.
He lobbied for a law signed in 1993 that bore his name and required background checks for handgun sales.
In 2000, Democratic President Bill Clinton renamed the White House press briefing room in his honour.
President Barack Obama described Brady as a “legend” at the White House and praised his warmth and professionalism and “the strength he brought to bear in recovering from the shooting that nearly killed him”.
“Since 1993, the law that bears Jim’s name has kept guns out of the hands of dangerous individuals,” he said. “An untold number of people are alive today who otherwise wouldn’t be, thanks to Jim.”
Brady, a lifelong Republican, served in the Nixon and Ford administrations before joining Reagan’s 1980 presidential campaign.
On 30 March 1981, John Hinckley Jr opened fire on the president’s party outside a Washington hotel, striking four people, including Brady and Reagan.
The former press secretary suffered brain damage, partial paralysis, short-term memory impairment and slurred speech.
Hinckley was tried and found not guilty due to insanity. Since the trial he has been committed to a Washington DC psychiatric hospital, but has been allowed to spend limited time at his mother’s home.
The so-called Brady Bill was signed into law by President Bill Clinton in 1993, years after the former press secretary began lobbying for stricter gun control rules.
“Every once in a while you need to wake up and smell the propane,” Brady said at the bill signing. “I needed to be hit in the head before I started hitting the bricks.” (BBC)