Farah, who was born in Somalia but moved to Britain as a child, said earlier on Sunday he was worried he would be unable to return to his home and family in the United States. He is currently training in Ethiopia.
"We understand from the statement released this evening by the Foreign and Commonwealth office that the executive order will not apply to Mo and we are grateful to the FCO for urgently clarifying the situation," a representative for Farah told the BBC. "Mo is relieved that he will be able to return to his family once his current training camp concludes."
The representative added that Farah still "fundamentally disagrees with this incredibly divisive and discriminatory policy."
"On 1st January this year, Her Majesty the Queen made me a Knight of the Realm," Farah said in a statement earlier on Sunday. "On 27th January, President Donald Trump seems to have made me an alien."
Farah is Britain's most successful track athlete, winning gold in the 5,000 and 10,000 metres at the London Olympics in 2012 and repeating the feat in 2016 in Rio, as well as at the World Championships in 2013 and 2015.
He is a British citizen, but his birthplace of Somalia is one of the seven countries subject to Trump's immigration restrictions.
The 33-year-old has been based in Portland, Oregon, for the past six years, where he said he had been working hard in training, paying taxes and bringing up his four children.
"It's deeply troubling that I will have to tell my children that daddy might not be able to come home - to explain why the president has introduced a policy that comes from a place of ignorance and prejudice," he said.
Trump announced a four-month hold on allowing refugees into the United States and a temporary ban on travellers from Syria and six other Muslim-majority countries, which he said would protect Americans from violent Islamists.
Farah said was been proud to represent Britain and to have received a knighthood from The Queen earlier this year. "My story is an example of what can happen when you follow policies of compassion and understanding, not hate and isolation," he said.
Trump's executive order triggered a storm of protest in the United States and abroad. British Foreign Secretary Boris Johnson said on Sunday it was "divisive and wrong to stigmatise because of nationality", and Britain would protect the rights and freedoms of UK nationals home and abroad.
(Reporting by Paul Sandle; Editing by Mark Heinrich and Peter Cooney)
