Police were called to the Llandegfan house last October after neighbours reported not seeing the Reverend Basil Bevan, 85, for sometime.
Officers found his body in a mummified state, the inquest heard. His wife was also living at the house.
The coroner recorded a verdict of death from natural causes.
Officers who spoke to the vicar's wife decided she was unwell and took her to hospital.
The inquest in Llangefni was told that in interviews Pauline Bevan described how her husband had a heart attack in November 2010.
Dewi Pritchard Jones, senior coroner for North West Wales, said there had been problems identifying the body.
A DNA comparison with the cleric's brother only gave a partial match because of the poor quality of the sample.
The coroner said he was satisfied the body was that of Dr Bevan who, on the balance of probabilities, died of heart disease.
Mr Pritchard-Jones said: "Neighbours had commented to a police officer that they hadn't seen the Rev Basil Bevan for some time and there was concern regarding his welfare.
"After some time Mrs Pauline Bevan came out of the property and there was a discussion with the police officers present. She appeared to be unwell and was taken to hospital.
"The police then went into the property, being concerned regarding Dr Bevan's welfare. When they went inside the property they found it was in a considerable state of disarray.
"On searching it they came across mummified human remains. The remains were not capable of visual identification."
He added: "For reasons that are not matters of concern for an inquest the body was allowed to remain at the property."
The cause of Dr Bevan's death was recorded as heart disease and the verdict was natural causes.
He was believed to have been ordained in 1955 and spent most of his career in Wales, serving in the Diocese of Swansea and Brecon before moving to north Wales in 1978.
The body of a retired vicar which was found in a house on Anglesey  had probably been there almost three years, an inquest has heard.