The body, believed to be that of Victoria Cherry, 44, of Fulwood, Lancashire, was found by Greater Manchester Police at a house in Toronto Street, Bolton, on Monday.
It was discovered following the earlier arrest of a 43-year-old man on suspicion of murder.
Ms Cherry has not been seen since October 2015.
Det Ch Insp Terry Crompton said: "We are continuing to support Victoria's family as they deal with this devastating news.
"The arrested man remains in custody, but I'm urging anyone with any information that would help our enquiries to get in touch.
"If you have information about Victoria's whereabouts since her disappearance in 2015, or if you hold any information about the events leading up to our discovery, please contact us as a matter of urgency."
Police investigating the suspected murder of a woman missing for 15 months have discovered a body.