The rollout was extended to over-40s at the end of April, and opens today to people in their 30s.
Those aged 38 and 39 are the first to qualify for a jab with around a million people being sent text messages that allow them to access the national booking service at the touch of a button with further invitations to follow in the coming days and weeks.
Dr John Pepper, chair of the new Shropshire, Telford & Wrekin Clinical Commissioning Group, said as of Monday(10), around 450,000 coronavirus vaccinations had been given in the county.
Of that, about 297,000 patients in Shropshire, Telford and Wrekin have now had at least one dose of the vaccine.
"It's going really well. There's no supply issues that I'm aware of at the present time," Dr Pepper said.
"We are performing very well against regional and national comparisons.
"It's really encouraging that it's rolling out like this."
He encouraged everyone to get their Covid jab when they are offered it and to make sure they attend for their second dose to get the best possible protection against the virus.
Dr Pepper says GPs have been put under pressure, as practices deliver Covid jabs on top of their usual workloads, but hailed the efforts of those involved.
He said: "There are pressures within primary care and among GPs and their teams.
"They have been balancing for quite some time the priorities of delivering general practice and also they are often involved in the delivery of the vaccination programme.
"We have to put on record a thank you to all those who are doing that because that's been a magnificent effort.
"The workload is high. Practices have to adapt to different ways of working.
"To keep patients safe, we've had fewer people through practices in face-to-face settings, although that is now switching on again and individual practices are gradually adapting the proportion of patients they see face to face.
"There is a pressure and I think primary care is responding magnificently to that. It's a challenge but it's why we go to work."
He also paid tribute to healthcare staff, local authorities and volunteers who have helped during the pandemic.
Waiting lists for planned operations and procedures at the county's hospitals have grown massively during the pandemic and plans are now being made to restore services.
Claire Skidmore, the CCG's interim accountable officer, said: "Our Covid admissions into hospital have slowed down so we are now starting to be able to open up capacity again, which is fabulous.
"What we're trying to do at the moment is refine those trajectories for the first half of the year but beyond as well.
"We've still got a lot of Covid restrictions in place in terms of social distancing which does put constraints on our ability to generate sufficient capacity to do lots of things but part of that planning process is also looking at how we prioritise capacity in the right places.
"We are planning for taking good strides against that recovery plan but this isn't a five minute fix.
"This is going to take a year or two to resolve in full, just because of the scale of that waiting list."