These will involve around 4,500 surgeries and 25,000 consultations and scans each year.
The single-storey facility will have MRI and CT scanners, but will not have capacity for overnight stays.
An 112-space car park will be built to the south of the site.
Neil Whittingham, from applicant WW Medical Ltd, said the facility would deliver “significant benefits”.
“The proposed development represents a vital enhancement to healthcare provision in Peterborough, addressing local needs and delivering significant clinical and economic benefits,” he told the meeting.
The facility was approved unanimously by councillors.