It signals the start of "Phase 2" of the vaccination programme - which involves offering vaccines to healthy adults aged under 50.
The move comes as it was announced that the Government has met its target of offering the vaccine to all adults over the age of 50.
Dr Richard Harling, Staffordshire County Council’s director of health and care, welcomed the news.
He said: “It’s great news even more people in are now able to join the thousands of Staffordshire residents who have already have their Covid vaccination.
“The vaccination programme has been a success in Staffordshire. It is one of the main things people can do protect themselves and their families from the virus and make sure the easing of lockdown keeps on track.
“The vaccine is safe and effective, and I strongly encourage all eligible people to book their slot as soon as they are able to do so.”
Across the Black Country and West Birmingham, 700,491 vaccine doses have been administered, and 698,952 in Staffordshire, the latest data shows.
Until now, the NHS had been focusing on offering vaccines to those deemed to be at highest risk - people over the age of 50, those deemed to be "clinically extremely vulnerable" and health and social care workers.
When its online booking system opened up to include people over the age of 45, the website crashed for many.
The announcement comes despite an earlier warning by the NHS in England of a "significant reduction in weekly supply" during April, meaning volumes for first doses would be "significantly constrained".
But a spokesman for the Black Country and West Birmingham CCGs told the Express & Star last week that enough doses have been secured during April to ensure all second doses and those eligible in cohorts 1-9 can get a vaccine.
Dudley North MP Marco Longhi said: "I'm clearly delighted we've made this progress with the over 45s now, which I believe is earlier than planned actually which shows not only have we got the infrastructure in place but we've also got the vaccine in stock to do so.
"We've sourced 17 million doses of the Moderna vaccine because of the issues with the production of the AstraZeneca vaccine, and the EU not playing ball basically.
"It's a really really positive move which clearly we've been able to make -- so please, if you're offered the vaccine, take it. It's our quickest way out of what we've been going through over the last 12 months."
The Prime Minister hailed the "hugely significant milestone" in the vaccination programme of reaching the April 15 target.
In a statement, Boris Johnson said that the Government remained on course to offer a first jab to all adults in the UK by the end of July.
The news comes as the Moderna vaccine was used for the first time in England.