Officers discovered the remains of a woman in dense woodland between the A89 south of Dechmont village in West Lothian and the M8 in Livingston yesterday afternoon.
The family of Heather McKay, 51, have been informed, Lothian and Borders Police said.
Police officers and mountain rescue volunteers found the body, which will be formally identified after a post-mortem examination.
A police source said the indication was that there were no suspicious circumstances surrounding the death.
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, exactly a week after her disappearance, police distributed thousands of leaflets and posters in the surrounding areas and spoke to commuters and parents dropping their children off at the local primary school.
Her children and sister also appealed to the public for information. Ms McKay's daughter, Andrea Waddell, broke down in tears at the press conference and was comforted by her 27-year-old brother Kevin.
Ms McKay's ex-boyfriend, Gary Winters – who, it was reported, had only recently split up with her – also made an appeal online for help in locating the missing woman.
Ms Waddell had said the break-up of her mother's relationship had affected her.
She added: "She's never gone before, it's completely out of character.
"I could be at work and she'd phone me. I never went two or three days without texting her.
"Mum would always leave a note if she was going out and she didn't take her phone."
Ms McKay was thought to have been wearing a light blue Berghaus rain jacket, jeans and a pair of brown Hi-Tec walking boots when she was last seen.
More than 20 calls were received from people who believed they may have seen her.
Trained officers also viewed more than 100 hours of CCTV footage from the surrounding areas about the time she went missing. Officers took more than 100 statements and carried out large-scale door-to-door inquiries in the streets near to where she was last seen.
Dozens of officers and members of the Tweed Valley Mountain Rescue searched the surrounding areas to check for any traces of Ms McKay, who was a keen walker and often hiked in the areas around Dechmont and Broxburn.
Police had described the public reaction to their appeals as "fantastic".
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