The Middlesbrough-born England international, 83, scored 141 goals in 238 games for the club between 1954 and 1964 and won six caps for his country.
He was also a promotion winner with Don Revie’s Leeds United before his career came to a premature end at Plymouth due to injury at the age of 30.
In a statement issued via the club website, Peacock said: “It saddens me to hear and read about many of my old teammates and opponents now suffering from Dementia.
"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.
“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.
“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. 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.