The Foreign Office confirmed following talks between Foreign Secretary Boris Johnson and Mr Trump, UK nationals born in any one of the named countries will be allowed into the United States.
Any British citizen travelling from a country not included in the seven banned states will "experience no extra checks regardless of your nationality or your place of birth", the Foreign Office said.
The executive order will also not apply to anybody with dual citizenship of one of the countries travelling to the US from outside those countries.
A Foreign Office spokesman added dual nationals could face extra checks if they are travelling from one of the seven countries and hold dual nationality with one of the countries.
He added: "The US has reaffirmed its strong commitment to he expeditious processing of all travellers from the United Kingdom."
Mr Trump's change in heart came after Theresa May ordered Mr Johnson to call his US counterpart to express concern over how the order would affect British citizens.
Donald Trump is continuing to back his travel ban despite global leaders condemning it
Earlier today Mr Trump defended his travel ban on seven Muslim-majority countries by saying he does not want the US to become like Europe – as his team warned judges cannot stop the order.
Mr Trump tweeted after waking up this morning: "Our country needs strong borders and extreme vetting, NOW.
"Look what is happening all over Europe and, indeed, the world – a horrible mess!"
He also ordered persecuted Christians be given priority over Muslims as refugees.
Homeland Security then said a temporary stay granted by a federal court will not stop the immigration ban from being put in place.
And senior White House official Reince Priebus revealed an alteration has been made to the order signed on Friday so US permanent residents are no longer affected.
He told NBC: "As far as green card holders, moving forward, it doesn't affect them."
In Britain, Theresa May has condemned the move and has ordered the Foreign Secretary and Home Secretary to call their US counterparts to urgently discuss the travel ban.
Boris Johnson and Amber Rudd have been told to call the United States following widespread condemnation of an emergency executive order which has meant hundreds of people with visas have been turned away from the US since Friday.
Citizens from Iran, Iraq, Syria, Sudan, Libya, Yemen and Somalia are banned for 90 days and all refugee admissions have been suspended for 120 days under the "extreme vetting" order.
Number 10 sources said the Prime Minister's order demonstrated how seriously she is taking the issue.
The Foreign Office told Express.co.uk officials are trying to clarify the details of the ban and how they affect British travellers to the US.
Mr Johnson and Ms Rudd have been told to raise particular concerns the ban could have on UK nationals.
Downing Street sources added Mrs May was "absolutely determined" to respond to the fears of Britons over the ban and she does "not agree" with the controversial measures.
Britons with dual nationality are part of the ban and there are concerns UK passport holders born in the seven designated countries may also be banned.
Olympic champion Sir Mo Farah, who was born in Somalia, and Iraqi-born Tory MP Nadhim Zahawi, are two of the most high-profile Britons affected by the ban.
Sir Mo, who has lived in the United States with his family for the past six years as he trains, earlier said: "On 1st January this year, Her Majesty the Queen made me a Knight of the Realm.
"On 27th January, President Donald Trump seems to have made me an alien."
Sir Mo Farah, Britain's most decorated Olympian, is not allowed back to the US where he lives
Earlier this afternoon Mr Johnson tweeted: "We will protect the rights and freedoms of UK nationals home and abroad.
"Divisive and wrong to stigmatise because of nationality."
It is unclear who Mr Johnson will speak to because Mr Trump's Secretary of State preference, Rex Tillerson, has not yet been approved by the full Senate.
A parliamentary source said the foreign secretary will urge Mr Trump's senior adviser Jared Kushner and adviser Steve Bannon, who was today given a seat at the National Security Council, to make sure UK dual nationals are exempt from the ban.
Other European leaders have joined Mrs May in condemning Mr Trump's travel ban, with German Chancellor Angela Merkel expressing her concerns to the President during a telephone call on Saturday.
She told him the global fight against terrorism was no excuse for banning refugees or people from Muslim-majority countries from entering the US.
The German leader also reminded him the Geneva Conventions require the international community to take in war refugees on humanitarian ground.
French foreign minister Jean-Marc Ayrault, said: "Terrorism knows no nationality.
"Discrimination is no response."
The Italian Prime Minister, Paolo Gentiloni, tweeted in Italian: "Italy is anchored to its values.
"Open society, plural identity, no discrimination. These are the pillars of Europe."
Scottish First Minister Nicola Sturgeon, tweeted: "For those asking my view on US State visit: would be wrong for it to go ahead while bans on refugees & citizens of some countries in place."
L'Italia è ancorata ai propri valori. Società aperta, identità plurale, nessuna discriminazione. Sono i pilastri dell'Europa
— Paolo Gentiloni (@PaoloGentiloni) January 29, 2017
Tens of thousands of people across the world have been protesting against the ban
Protests have been taking place outside US airports and across the world.
A UK petition for a planned state visit to Britain by President Trump later this year is calling for it to be scrapped because it "would cause embarrassment to the Queen".
Being President Trump: Key Moments
Fri, January 27, 2017
Inside Donald Trump's first week in the White House.
1 of 12
Trump speaks briefly to reporters as he arrives aboard Air Force One at Joint Base Andrews
The online petition had already gained nearly 380,000 signatures by 4pm.
Parliament will now have to debate the petition as it has received more than 100,000 signatures.
An "emergency demo" against Mr Trump's travel ban planned for 6pm on Monday outside Downing Street has been organised by left-wing journalist Owen Jones.
A total of 10,000 people on Facebook have said they will attend the demonstration which Mr Jones said is also in protest against Mrs May deciding "to ally herself with Donald Trump's bigoted misogynistic government".
Texas mosque burns down after Trump imposes Muslim ban
Thousands petition to ban Trump from visiting UK
Zahawi: Trump's Muslim ban is 'discriminating and sad'
Mr Trump's team has rallied behind his decision to ban citizens from Muslim countries, however many of them were very clear in December 2015 they were against a Muslim ban.
Many of them rejected Mr Trump's proposal for a "total and complete shutdown of Muslims" entering the US.
Vice-President Mike Pence, at the time said: "Calls to ban Muslims from entering the US are offensive and unconstitutional."
And now-Chief of Staff Reince Priebus, said: "I don't agree. We need to aggresively take on radical Islamic terrorism but not at the expense of our American values."
Earlier today, he said: "We apologise for nothing here."
Senior Majority Leader Mitch McConnell, said Mr Trump's remarks were "completely inconsistent with American values" and said a ban would be "unworkable".