However, Oxford University’s Migration Observatory and think tank British Future have warned that new immigration rules could hit social care and hospitality businesses in the UK.
Home Office figures reveal that by the end of September 2020, 5,980 people successfully applied to continue living in the Shropshire Council area after December 31, as well as 9,220 in Telford & Wrekin
In Powys there were 1,770 successful applications.
European Union nationals wishing to continue living in the UK must apply under the EU Settlement Scheme by June 30 2021.
Those who have lived in the UK for five years and meet the criteria, can receive settled status and remain in the country indefinitely.
Those who have lived in the country for less time can receive pre-settled status, which allows them to remain for a further five years. They can later apply for settled status.
Of 6,120 applications dealt with in Shropshire between August 2018 and September 30 2020, 3,520 granted applicants settled status and 2,460 pre-settled status.
For Telford 9,440 applications were dealt with over the same period, with 4,830 applicants granted settled status and 4,390 pre-settled status.
In Shropshire around 140 applications were either refused, withdrawn, or invalid, as well as 220 in Telford & Wrekin.
Figures are rounded to the nearest 10.
In Shropshire, the highest number of applications was submitted by residents from Bulgaria (1,620), followed by people from Poland (1,490) and Romania (1,030).
For Telford it was residents from Poland (2,990), followed by people from Romania (1,820) and Italy (940).
In Powys 1,190 people were granted settled status and 580 pre-settled status, with around 40 applications refused, withdrawn, or invalid.
The most applications for Powys came from people from Poland (750), followed by people from Bulgaria (230) and Romania (200).
Across the UK, 3.9 million applications have been made under the EU Settlement scheme since it was launched – 56 per cent of applicants received settled status, 41.6 per cent pre-settled and only 0.4 per cent were refused.
Across the UK the highest number of applications come from residents originally from Poland with 750,000, followed by people from Romania with 640,000, and Italy with 390,000.
Sunder Katwala, director of British Future, said new rules requiring immigrants to meet a £25,400 salary threshold may pose issues for some sectors, although foreign graduates will be allowed to work after they study.
He said: "Despite the additional bureaucratic processes and visa fees, EU migration will continue for graduate professionals in areas like law, science and academia.
"The Government has committed to allowing the NHS to recruit the staff it needs – but has not done the same for social care.
"The most significant impacts are likely to be in social care and hospitality, for roles paying below those salary bands."
He added that there should be sustained scrutiny over time to ensure that those who have pre-settled status can successfully convert should they wish.
Madeleine Sumption, director of the Migration Observatory, said: "The UK has certainly become less attractive to EU migrants since the 2016 referendum: over the past three years, EU immigration has fallen substantially.
"The Government has introduced a system that is designed to be easy for EU citizens to apply to, securing their residence rights in the UK.
"For most EU citizens, the process will be very straightforward, but there is a strong risk that some people will fall through the cracks – particularly among vulnerable groups such as victims of abuse and exploitation."