Telford & Wrekin Council leader Shaun Davies says Stirchley Medical Practice and Dawley Medical Practice are planning to start giving Covid jabs in the next couple of days.
He says Hollinswood & Priorslee Medical Practice is planning to start vaccinating by the weekend and Charlton Medical Practice, in Oakengates, by the end of the week.
People are being asked to be patient and wait until they are contacted by the NHS and invited to an appointment.
Councillor Davies added: "Many people have contacted me about those who are restricted to home.
"Many GP practices will be conducting home visits.
"Be sure to tell the GP if this applies to you or a family member."
Telford International Centre also opened its doors as a vaccination centre on Monday, kicking off by jabbing health and social care staff.
It will open to the public on Thursday.
In the next few weeks, other sites due to open as vaccination centres are expected to include Ludlow Racecourse, the indoor bowling centre at Shrewsbury Sports Village and Whitchurch Civic Centre.