The woman directing the programme, Angie Wallace, said vaccines should have been offered to the most vulnerable by the middle of February.
She said the team was working tirelessly.
"The NHS in Shropshire, Telford and Wrekin is working incredibly hard to deliver the Covid-19 vaccination to the most vulnerable local people, at the same time as providing care to all those who need it and whilst coping with the rising number of Covid-19 cases and winter pressures," she said.
"This immense local effort across the Shropshire, Telford and Wrekin health and care system has led to the rapid roll out of the programme across our communities."
She said that, in just a matter of a few weeks, GP-led local vaccination services have been launched across all the primary care networks, hospital hubs, and roving vaccination teams for care homes and the housebound.
"All residents in older people care homes have been offered the first dose of the vaccine, over 90 per cent of over 80s, and 56 per cent of the 75 to 79-year-olds have been vaccinated.
"Very good progress is being made to meet the target of vaccinating the first four priority groups by the middle of February."
"We have made incredible progress in a very short space of time since the vaccination – which is safe and effective – first became available. We’d like to thank the entire Shropshire, Telford and Wrekin Covid-19 vaccination team who have done an incredible job to deliver what is the largest vaccination programme in our history."
She said that the roll out was good news, but said people afford to be complacent.
"The large increase in cases hospitals are seeing and the emergence of a new variant of the virus also shows that we cannot let our guard down now, and even those who have received a vaccine still need to follow all the same guidance as everyone else to help protect others."