Officers discovered the body of a woman at around 1.30pm in dense woodland between the A89 south of Dechmont village in West Lothian and the M8 in Livingston.
The family of Heather McKay, 51, have been informed, Lothian and Borders Police said.
Search teams of police and Tweed Valley Mountain Rescue found the body which will be formally identified after a post-mortem examination.
Ms McKay was last seen at her friend's home in Craiglaw, Dechmont at around 7.30am on Friday August 24. Her disappearance was described by her daughter as out of character.
Last Friday, on the one-week anniversary of her disappearance, police distributed thousands of leaflets and posters in the village and surrounding areas and spoke to commuters and parents dropping their children off at the local primary school.
Her children and sister also appealed to members of the public for information.