The 68-year-old began his career at St Mirren before moving to Elland Road in 1972, winning the First Division two years later and playing an important role in their run to the 1975 European Cup final.
McQueen scored five goals for Scotland, earning 30 caps en route to the Hampden Hall of Fame, and also enjoyed a successful time with Manchester United before moving into management with Airdrie and coaching at Middlesbrough.
The defender was also a popular TV pundit with Sky Sports and Scottish Television.
A statement released by his wife Yvonne and daughters Hayley and Anna and son Edward highlighted the potential risks of persistent heading of the ball – and revealed the popular defender stayed behind at training to practice aerial scenarios with goalkeepers.
They told PA news agency: "In January, Gordon McQueen, our dad, was formally diagnosed with vascular dementia. As a family we felt it was important to let people know, particularly if raising awareness can help others in similar situations.
"Whilst we've found it hard to come to terms with the changes in dad, he has no regrets about his career and has lived life to the full. He had unforgettable experiences in his playing days with Scotland, Manchester United and Leeds United, and also took so much from his coaching and TV work in more recent times.
"Football has allowed him to travel the world and experience things he could only have dreamed of.
"But he wants other footballers of today's generation to know there may be risks with persistent heading of the ball.
"Dad scored some important goals in his career and memorable headers but used to stay back in training, heading the ball to the goalkeeper for practice over and over. He does wonder if this has been a factor as his symptoms appeared in his mid-60s.
"The last year in and out of lockdown has been tough as dad is such a sociable person and thrives off company.
"Social interaction is key for someone with dementia and he has been deprived of this for so long. He is fully aware of his friends and family still and his memory of all things football is sharp, but his cognitive functions are not the same.
"We don't want people to be surprised by his condition or to ask for interviews or autographs which he is not able to do any more.
"Whilst he is looking forward to seeing people again after lockdown and getting the social aspect of life back, we know people will see a big difference in his health so wanted to be transparent.
"We thank everyone in advance for their understanding and hope sharing this news will help dad to face the future in a positive way."
McQueen's former Leeds team-mate Jack Charlton died with dementia last year and it was recently confirmed that Sir Bobby Charlton has been diagnosed with the disease. The brothers' 1966 World Cup-winning team-mate Nobby Stiles died with dementia last year.
Two independent research studies, supported by the FA, are currently examining former players and early signs of neurocognitive degeneration. H
After research, heading by under-12s was also banned in Scotland and England last year.