You could use either of those it would depend upon the circumstance and what perspective you are telling the patient. But we would not say disease and cancer together, we would say condition/illness. To use diagnosis, a normal natural way is to say. "The diagnosis is cancer" "The hospital tests show/reveal cancer" "The hospital/consultants diagnosis is cancer" "The hospital tests found cancer" cancer is a very general broad term used by lay people and not by doctors hospitals reports etc. Their reports would say something far more specific and medical to indicate to the G.P a doctor exactly what is wrong, and the doctor or the hospital/consultants would then at a later date explain your condition.

To use “diagnose” as a verb, you could say: “My doctors have diagnosed me with cancer.” “I tried to diagnose myself by researching my symptoms online, but it didn’t work.”