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, 2,820 people successfully applied to continue living in the area after December 31.
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 2,910 applications dealt with in Scarborough between August 2018 and September 30 2020, 1,430 granted applicants settled status and 1,390 pre-settled status.
Around 80 applications were either refused, withdrawn, or invalid.
Figures are rounded to the nearest 10.
In Scarborough, the highest number of applications was submitted by residents from Poland (1,120), followed by people from Romania (1,040) and Latvia (140).
There were also around 40 applications from people who are not from the European Economic Area, but qualify for the scheme. Those qualifying include family members of EU citizens living in the UK.
Across the UK, 3.9 million applications have been made under the EU Settlement scheme since it was launched – 56% of applicants received settled status, 41.6% pre-settled and only 0.4% 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."