GPs in the city are working to provide vaccinations for care home residents and patients over 80-years-old.
There are 17 sites for the jabs now open across the city, with a large vaccination centre at Elland Road expected to open in the coming weeks.
Vaccinations are by appointment only.
People should not contact their GP about a vaccination unless asked to do so and they should not attend any vaccination site without an appointment.
Dr Phil Wood, lead for the West Yorkshire Covid-19 Vaccination Programme, said: “It is great news that we will be able to protect more vulnerable people.
"We are working with partners across West Yorkshire to make sure people can get their first vaccination as quickly and easily as possible and are ready to expand the rollout as fast as supplies become available."
The Government has set the target for a vaccination centre to be less than 10 miles away from every resident in the UK.
The Yorkshire Evening Post has teamed up with sister titles across the country to urge Prime Minister Boris Johnson to go one step further - to deploy the country’s network of 11,000 pharmacies to ensure that every citizen is only a short walk away from a centre.
Our campaign also requests further reassurance for local communities from the Government and more easy-to-access information on the vaccine programme and its progress.
This is the location of the 17 vaccination centres now open across Leeds:
