North Lanarkshire Council moved all tenants from Anderson Tower in Motherwell on Thursday as a precautionary measure after concerns were raised.
The substance was disturbed during mains cabling replacement work that was being carried out at the tower by ScottishPower, the council said.
Residents stayed in hotels, temporary council accommodation or with friends and family over the weekend while the clean-up continued. Meal and accommodation costs for those in hotels have been paid by ScottishPower's contractor.
Some asbestos dust had been found in halls and lobbies of the block but tests have now found it to be clear.
The council's operations manager Stephen Llewellyn said: "The decision to allow residents to return to their homes was taken only after the council was satisfied the building had been properly deep-cleaned and test results showed clear."
An investigation is being carried out into the incident.