The President-elect’s key aides told the Foreign Secretary in America that Britain would be "front of the line" when it became possible to negotiate.
Mr Johnson travelled to the States to build relations with Mr Trump’s team ahead of the Prime Minister’s trip due later after this month.
Speaking after his meetings, Mr Johnson said: "Clearly, the Trump administration-to-be has a very exciting agenda of change. One thing that won't change though is the closeness of the relationship between the US and the UK.
"We are the number two contributor to defence in Nato. We are America's principal partner in working for global security and, of course, we are great campaigners for free trade.
"We hear that we are first in line to do a great free trade deal with the United States. So, it's going to be a very exciting year for both our countries."
Mr Johnson first met Mr Trump's son-in-law, Jared Kushner, set for a top job in Washington, and Steve Bannon, the US president-elect's strategist and controversial far-right media boss.
It was the first formal face-to-face meeting between members of the incoming US administration and a UK minister. Officials have said US foreign policy towards Syria, China and Russia were also discussed.
Then yesterday Mr Johnson was in Washington to meet key congressional politicians Newt Gingrich, Paul Ryan, Ben Cardin and Mitch McConnell.
Barack Obama had angered Brexiteers by saying during the EU referendum campaign that the UK would be "back of the queue" for a trade deal if it quit the European Union.
Mr Johnson's trip comes after the Government was embarrassed when Nigel Farage became the first UK politician to meet Mr Trump last year.
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