It is thought Linda Weir, 58, from Thornhill, Dumfries and Galloway, was swept away by the swollen waters of Burnsands Burn, which joins the River Nith.
The alarm was raised on April 5 after the quad bike was found in the water near her Crairieknowe Farm home.
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Hide AdA major search, which included 30 rescue specialists, was carried out over two days.
Police today confirmed the body discovered in the River Nith yesterday was that of the missing woman.
A Dumfries and Galloway Police spokesman said: "The body of a woman found in the River Nith at Carnsalloch on Thursday is that of the missing woman Linda Weir, from Crairieknowe Farm, Thornhill, who went missing from her quad bike as she crossed Burnsands Burn. "
A report has been sent to the procurator fiscal.