Officials were encouraged by the Secretary of State to write to their staff to apply for settled status.
It comes as the government is launching an EU Settlement Scheme in March this year, but has trialled the system for health and care workers.
The scheme means EU citizens can apply to continue living in the UK after June 30, 2021.
Now, United Lincolnshire Hospitals Trust has confirmed they have agreed to meet the costs of registering EU nationals in their workforce.
ULHT, which employs 300 EU nationals plus 50 bank staff, is set to spend between £15,000 to £20,000 to register its workers.
The EU Settlement Scheme will allow nationals who have lived here for five years or more to register for settled status.
Those who have lived in the UK for less than that amount of time can apply for pre-settled status.
Each application will cost £65 for adults and £32.50 per child in order to register.
The UK is set to leave the EU on March 29, 2019.
Health secretary, Matt Hancock MP, said in a letter to health officials that he “strongly encouraged” them to use the scheme in order to give staff “certainty”.
“There is no obligation for EU nationals to register early,” he said.
“However it is an opportunity for many to get this certainty earlier, and I would strongly encourage you to publicise this to your health and care staff who are EU nationals.”
A spokesperson for ULHT said: “At United Lincolnshire Hospitals NHS Trust we value every member of staff, including those working with us from the EU.
“We have been actively engaging with our staff from the EU and offering them full support around the arrangements for continuing to work at the trust as they play a very important role in maintaining essential services.”