A devoted lifelong fan of the team, he joined the board in 2005 and took over as chairman in 2013 following the resignation of Peter Hill-Wood.
Keswick, a prominent figure in the financial sector and a director of the Bank of England, presided over the club for seven years.
“Everyone at Arsenal who knew Sir Chips will miss him terribly,” the club said in a statement.
“We extend our deepest sympathies to his wife Lady Sarah and their children David, Tobias and Adam.”
