Ann Grisman, from Hereford, disappeared after arriving in Wellington by taxi on 28 November.
The body was discovered by a member of the public on a building site at Longforth Farm, on the outskirts of Wellington, at about 09:30 GMT.
Police said Mrs Grisman's death was not at this stage being treated as suspicious and her family had been informed.
Police searching for a missing 80-year-old woman have found a body.