LeMond, 60, first won the Tour de France in 1986 and then followed it up with victories in 1989 and 1990.
"I have been diagnosed with chronic myelogenous leukaemia," he said in a statement on his website.
"Fortunately, it is a type of cancer that is treatable, and it is a type of leukaemia that is not life-threatening or debilitating.
"Following a series of tests and a bone marrow biopsy, which was completed last week, I received my formal diagnosis last Friday.
"No one ever wants to hear the word cancer but, admittedly, there is great relief, now, to know why I was feeling poorly."
LeMond also won the World Championships in 1983 and 1989 before retiring from competition in December 1994.
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