The property on Tettenhall Road, close to the junction with Newhampton Road West, has been empty for some time.
At a meeting of the city’s planning committee this week members raised no objections to the proposals.
The council had earlier received nine letters of objection to the application, citing loss of privacy, a possible rise in crime and increased traffic as concerns.
Assistant planner Laleeta Butoy said the development would include 15 new car parking spaces in the front courtyard which would be needed to accommodate the demand expected to be generated by the practice.
“The scale of the development is considered not to have any unnecessary adverse impact on nearby residences, nor highway or pedestrian safety, and provides adequate protection to trees,” she added in a report to the committee.
A two-storey rear extension was previously added to the property when it was in use as a dwelling house.
Although the type of medical practice was not specified, members heard the centre would be fitted with four treatment rooms.