Watkins is a director of Lancashire County Cricket Club and served on United's board for 28 years as well as acting as a lawyer for the club, which included representing Rio Ferdinand during the 2003 hearing which resulted in an eight-month ban for missing a drugs test.
“I am delighted Maurice has agreed to accept the role of chairman of British Swimming," said chief executive David Sparkes.
"He brings a wealth of experience in sport to the board and his leadership will, I am sure, enable the board to be more focused as we take on the lessons from London and prepare for Rio to achieve medal success across the sport.
“We face some challenges and I am sure Maurice will drive forward our plans and I look forward to working with him over the next four years."
Watkins is a joint senior partner of law firm Brabners Chaffe Street and a director of the British Association for Sport & Law.
"I am delighted to have been asked to become chairman of British Swimming," he said. "It is an honour and a privilege.
"I look forward to working alongside people who are an inspiration in such an outstanding sport."
Watkins's other roles include interim chairman of the Rugby Football League - having carried out a Governance Review - and chairman of the Greyhound Board of Great Britain.
- Board & Management Changes
- Sports & Recreation
- Lancashire County Cricket Club
- Rio Ferdinand