The discovery was made yesterday at Dale Avenue in Cambuslang.
Police are thought to have been alerted to the discovery by workmen in the area.
It is not yet clear how long the remains had been there or whether they were male or female.
An investigation is under way to establish the circumstances surrounding the death and the spot has been cordoned off.
A police spokeswoman said: “Police Scotland can confirm that inquiries are under way following the discovery of human remains found at Dale Avenue, Cambuslang, on Tuesday April 7.
“Further examination of the remains will be carried out.
“A search of the area is currently under way and officers are conducting enquiries to establish the identity and circumstances surrounding the discovery.”
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