The 83-year-old won six caps for England and played 238 games for Middlesbrough between 1954 and 1964.
Peacock also played under Don Revie in a promotion-winning Leeds side, before his career was brought to a premature end through injury at the age of 30.
“It saddens me to hear and read about many of my old team-mates and opponents now suffering from dementia,” Peacock said in a statement on Middlesbrough’s website.
“I was diagnosed in 2018 with vascular dementia/Alzheimer’s disease. At the time, it didn’t really sink in, but as time has gone on I realise I’m not quite the man I was a few years ago.
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“Although my career was sadly and devastatingly cut short due to injury, I actually feel lucky. Perhaps if I had carried on playing, I might have been affected at a much younger age.”
There have been a number of calls recently to football authorities to establish a fund to support ex-players suffering from neurodegenerative disease.
England World Cup winners Nobby Stiles, Jack Charlton, Ray Wilson and Martin Peters are among those to have died from the disease, while former Liverpool midfielder Terry McDermott was diagnosed recently.
“Much has been debated about the weight of the old footballs, especially when wet, possibly contributing to the number of players now presenting with the disease,” Peacock added.
“I’m not sure about that, but it really was like heading a cannonball at times! Having said that, I wouldn’t change a thing.
“I love the game and am extremely proud to have been fortunate enough to play for my hometown, the mighty Leeds United and of course, my country.
“I am, and intend to stay, positive. I enjoy going to the Riverside, being involved with the club, watching home games and catching up with everyone. I really missed it during lockdown.
“There are naturally good days and bad. The good days far outweigh the bad at the moment and I’m hoping it stays that way for a long time to come.
“I am aware that there is ongoing speculation about my condition which fortunately has been progressing slowly.
“My family and I are hoping that, by publicly acknowledging my illness, it will raise awareness and encourage further research and support for everyone affected by this terrible, progressive disease.”