American Evan Szymanski and his French wife Sophie, who live in Somerby, came to this country in 2012 with their two sons, now aged seven and four.
They decided they wanted to live in the UK and applied to the Home Office for permission to stay.
But the Home Office rejected their application following concern about whether they were ‘self sufficient’.
Mr Szymanski and his wife – who have since had another son, now aged 17 months – then successfully appealed against the rejection at an Immigration and Asylum hearing in Nottingham.
However, the Home Office appealed against that decision and a hearing was arranged at Birmingham.
Now, at the latest Upper Tribunal Immigration and Asylum hearing in Birmingham, it was finally confirmed the family can stay.
Mr Szymanski (34), who is an English and special needs teacher, said: “For quite a while the overwhelming emotions were rage and confusion, now it is just relief.
“We are ready to move on with our lives and forget about it.”
He said the hearing happened on March 3 and the following weekend “was the first time we relaxed since we moved here”.
Mr Szymanski said they are happy in Somerby.
“It is the first time we have felt at home. We are part of the community.”
At the Birmingham hearing, Mr David Mills, who was representing the Home Office, told the tribunal judge Mr John McCarthy that his department had no objection against the couple remaining in Britain after being told that Mr Szymanski was teaching children with special needs in Leicester and that Mrs Szymanski was running an online sales business.
Mr McCarthy confirmed the couple can stay.
Mr Szymanski, who comes from New York, said he and his wife were relieved and delighted with the decision following the judge’s decision.
Mr Szymanski said: “We like it here and we want to stay.
“In my view this whole process was entirely unnecessary - we should never have been looked at.
“We have always been here with the European laws.”