Under the EU Settlement Scheme people from European countries who want to continue living in the UK after 30th June 2021 will have to apply to do so.
Those aged 16 and over will be charged £65 to apply and £32.50 will need to be paid for those under the age of 16.
The Rt Rev Paul McAleenan, Catholic Bishop for the Diocese of Westminster said EU citizens living in the UK have faced "profound uncertainty and insecurity about their future" since the 2016 referendum.
"Although the reassurances offered by senior politicians are important, people have been given far too little information or binding commitments about their right to stay," he said.
"For some this has been worsened by the appalling rise in hate crime, which has left them feeling unwelcome or even threatened in the country that has become their home."
The Church has said it "stands in solidarity" with all EU citizens who have made their home in the UK and "as the majority are themselves Catholic this is a special pastoral concern for us".
People with indefinite leave to remain in, or enter, the UK or with a valid 'UK permanent residence document' will have to apply if they want settled status, but they won't be charged.
Irish citizens don't need to apply.
Those applying from April 2019 to move from pre-settled status to settled status and children in local authority care will also be exempt from the fee.
Bishop Paul said the Church "strongly oppose the decision to charge people for securing the rights they already have".
He added: "We also expect that some people, particularly those who are already vulnerable, may face difficulties in practically accessing the scheme, leaving their immigration status at risk.
Finally we urge the whole Catholic community to take up Pope Francis' call to welcome, protect, promote and help to integrate everyone who has made their home here - with particular concern at present for our European brothers and sisters."
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