Greg Monks, 38, was last seen in Albufeira during the early hours of Wednesday, 28 May, while enjoying the first night of a five-day stay.
A major search was launched for the Cambuslang man, with his parents and girlfriend flying out to Portugal to also provide assistance.
His sisters, Jillian and Carlyn, previously spoke to Sky News about the family’s devastation at his disappearance.
Speaking to The UK Tonight with Sarah-Jane Mee before the police’s announcement, they described their brother as a “big part of our family”.
Local police confirmed on Wednesday that a body had been found in the Cerro de Aguia area, where Mr Monks was believed to have been last seen.
A statement by Portuguese police said the body was located on a vacant and uneven lot.
The force added: “After the competent judicial inspection has been carried out, the body will be removed to the area’s legal medicine office for an autopsy to be performed.”
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Mr Monks was earlier described by his sisters as a “real family man”.
When his family arrived in Albufeira, police told them they had spotted Mr Monks twice on CCTV footage walking around the residential area.
The area where he was last seen – more than an hour’s walk from the Albufeira Strip – had a lot of rough terrain, including rocky outcrops and cliffs.
The Foreign, Commonwealth and Development Office (FCDO) said it was supporting Mr Monks’ family and was “in contact with the local authorities”.
