"It's a huge loss for everyone. He was a family man, a true gentleman and Swansea City through and through," said Jenkins.
"There was nothing he didn't know about the club and thanks to his expertise, the history of Swansea City will stand the test of time."
He was a prolific author and among his books were Swansea Town/City 1912-82, and Ivor Allchurch, a biography he wrote with Peter Stead, plus the Official Biography of the Swans published in 2000.
Professor Farmer's love of the Swans began after being taken to the old Vetch Field as a six-year-old in 1938.
He became a non-executive club director in August 1997 with responsibility for the club's youth development structure. He stepped down as a director in October 2001 to become club president, a role in which he became highly respected and regarded.
"The game has lost one of its great ambassadors and our thoughts are with his family at this sad time," added Jenkins.
Source: BBC Sport
Source: BBC Sport