In a statement, the president referred to Mr Brady as a "legend" and sent his condolences to his family.
Jim is a legend at the White House for his warmth and professionalism as press secretary for President Reagan; for the strength he brought to bear in recovering from the shooting that nearly killed him 33 years ago; and for turning the events of that terrible afternoon into a remarkable legacy of service through the Brady Campaign to Prevent Gun Violence.
– Barrack Obama
Mr Obama said since 1993, the law that bears Mr Brady's name has kept guns out of the hands of "dangerous individuals", adding: "An untold number of people are alive today who otherwise wouldn’t be, thanks to Jim.
"Our thoughts and prayers are with Jim’s wife Sarah, who has been Jim’s steadfast partner in advocacy, and their children Scott and Melissa."
Former first lady Nancy Reagan has called former ex-US press secretary James Brady "the personification of courage and perseverance," NBC reports.
Mr Brady, who was wounded during the 1981 assassination attempt on president Ronald Reagan, has died aged 73.
In the short time he was able to serve as White House press secretary, Jim brought sharp instincts, integrity and energy to one of the most demanding jobs in Washington. What a shame that he was not able to serve as we had hoped for longer. Jim was the personification of courage and perseverance. He and Sarah never gave up, and never stopped caring about the causes in which they believed.
– Nancy Reagan
Mrs Reagan also recalled the "unspeakable fear" she shared with Brady's wife, Sarah, at the hospital after the assassination attempt, saying "the bond we established then was unlike any other."