The 63-year-old woman has been arrested on suspicion of murder.
She walked into Cheadle Heath Police Station in Greater Manchester on Sunday and told police she had killed a man "a number of years ago".
The woman said she buried him in the garden of a house in Reddish, near Stockport.
Following door-to-door inquiries, police discovered human remains on Tuesday evening which they believe are those of the man, Kenneth Coombes.
The man's family have been informed but the remains have not yet been formally identified.
Mr Coombes was in his late 80s in 2005.
Detective Inspector Dan Clegg, of Greater Manchester Police's major incident team, said: "The investigation is still in its early stages and many questions still need answers.
"We will continue our work at the scene through the night and hope in the coming days we can piece together the exact circumstances surrounding the man's death.