Coun Graham Latty and Lady Mayoress, Coun Pat Latty, visited youngsters taking parts in sports and career development work last night.
It follows a Civic Reception for the club last month, during which the councillors expressed an interest in attending the Hillidge Road institution.For more than 75 years, it has been helping young people to achieve their full potential.
Club trustee Andrew Beadnall said: "They loved it. Afterwards, when we were having tea, the Lord and Lady Mayoress said they've absolutely loved their visit."
"The Lady Mayoress is a councillor and she had visited the club some years ago. The Lord Mayor said, 'My wife has spoken about this club ever since she came, and now I can understand what she was on about'."
During a tour of the site host Dennis Robbins, the club's chief executive officer, showed the pair boxing, gymnastics, ballet dancing as well as other activities including post-16 career workshops in areas such as mechanics and plumbing.
"They actually had a little punch themselves, on the punchbags, the Lord and Lady Mayoress," said Mr Beadnall.
The club was set up by Dr John Wyllie, a local GP, who first opened it in 1940.
During the war when fathers were in the army, there was an increase in antisocial behaviour, which was becoming a problem in south Leeds.
He wanted to provide local boys with the chance to channel their energies into something positive, and with the support of the community he formed the Hunslet Club.
It now has some 2,500 members, opens seven days a week and welcomes more than 250 young people through the doors every day.
As well as 40 full-time staff, 150 people also volunteer at the club.
Coun Latty said: “Our visit was quite a revelation. We were hugely impressed with the scope, and variety of offers for the young members; everything from ballet through to car and bike mechanics, plumbing and joinery to boxing, rugby and football.
"We had a lovely warm welcome and were shown absolutely everything and met many of the dedicated people who make this club the icon that it is.”