The Foreign Secretary hit out at Labour MPs who had condemned the President's ban on immigrants travelling to the US from Muslim-majority countries in what has widely been branded a "Muslim ban".
Mr Trump has also said the US will not take any Syrian refugees for a period of 120 days.
Speaking to MPs, Mr Johnson said the ban will not affect British passport holders as he branded discrimination on grounds of nationality "divisive and wrong".
The Foreign Secretary told MPs that Britons "remain welcome to travel to the US" and the country's embassy in London had confirmed President Trump's executive order would make "no difference" to British passport holders.
Mr Johnson said: "The general principle is that all British passport holders remain welcome to travel to the US.
"We have received assurances from the US embassy that this executive order will make no difference to any British passport holder, irrespective of their country of birth or whether they hold another passport."
He added: "This is not our policy, nor is it a measure that this Government would consider. I have already made clear our anxiety about measures that discriminate on grounds of nationality in ways that are divisive and wrong."
Labour backbencher Mike Gapes could be heard to shout "show some backbone" and "where's your spine?" as Mr Johnson updated MPs about Mr Trump's immigration policy.
The Foreign Secretary acknowledged the US policy was "highly controversial" but stressed the "vital importance" of the transatlantic alliance to the UK.
However he was strongly criticised by opposition MPs for failing to take a tougher line with the new administration.
Shadow foreign secretary Emily Thornberry said: "When it comes to human rights, when it comes to women's rights, when it comes to torture and the treatment of minorities, President Trump is already descending down a very dangerous slope.
"When that happens we need a prime minister who is prepared to tell him to stop, not one who simply proffers her hand and silently helps him along."
Veteran leftwinger Dennis Skinner compared the US President with Hitler and Mussolini, accusing the Government of being "hand in hand with another fascist - Trump".
Mr Johnson said such comparisons between the elected leader of the US and the "tyrants of the 1930s" were "inappropriate".
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