Keswick takes over from Peter Hill-Wood, 77, who has decided to stand down from the board after suffering a heart attack last year.
Hill-Wood had been at the helm since 1982 and his father Denis and grandfather Sir Samuel ran the club before him in a family dynasty stretching back to 1927.
The change comes at a critical time as manager Arsene Wenger decides whether to spend the transfer kitty chief executive Ivan Gazidis insists is available in what he predicts could be a "big summer" for the Gunners.
The current close season is the first in years that the Gunners are not expected to lose one of their best players, while Manchester United's Wayne Rooney and Real Madrid's Gonzalo Higuain have both been linked with possible moves to the Emirates Stadium.
The appointment of 73-year-old Keswick is a safe one in financial terms considering he is a former director of the Bank of England and a former chairman of Hambros Bank.
An Arsenal statement insisted Keswick, who has been on the club's board for eight years, would be working closely with Gazidis on the club's football and business ambitions.
Sir Chips, full name Sir John Chippendale Lindley Keswick, is a member of the Keswick family which control Hong Kong company Jardine Matheson.
He is an old Etonian and is currently a non-executive director of a number of companies including DeBeers Sa, Investec Bank and Persimmon plc.
Arsenal majority owner Stan Kroenke said: "I am delighted that Sir Chips has agreed to become chairman. He has a well respected track record in business and he will provide further direction and support in our ambition to compete at the top of the game here and in Europe and to win trophies."
Arsenal have not won a trophy since Keswick joined the board in 2005 but his first role as chairman was to pay tribute to Hill-Wood.
Keswick said: "I am sad to see Peter standing down due to his health and we all hope he continues well in his recovery. The Hill-Wood family has made an extraordinary contribution to Arsenal over many decades. They have been central to the club's many achievements during this time.
"I am greatly honoured to have been appointed chairman of Arsenal football club. This is one of the great clubs in the game, recognised and loved by millions. I am looking forward to leading the club to future success."
Hill-Wood perhaps will be best remembered for driving through Arsenal's move from Highbury to the Emirates Stadium, a move which has required the club to act with financial prudence in recent times but has also provided a state-of-the-art facility for decades to come.
Hill-Wood said: "This has been a difficult decision as Arsenal football club has been a huge part of my life. Although I am feeling better I feel this is the right time for me to stand down.
"I would like to thank our majority owner Stan Kroenke for the respectful and dignified way he has handled this and I know Sir Chips is the right person to take the club forward."
Kroenke paid his own tribute to Hill-Wood. "Peter has been a wonderful custodian of this club," he said. "He has been a member of the Arsenal board for 51 years and his vision and steadfastness have been central to the successes of this great club over that time.
"Peter will be sorely missed but we will be ensuring we recognise his many contributions to the club in an appropriate way."