Relations between the UK and the US are going to be "sensational" now Boris Johnson is in Downing Street, America's ambassador to the UK has said.
Woody Johnson told the BBC the two had a lot in common in their leadership style and desire to "get things done".
He played down the PM's criticism of Mr Trump when he was London mayor, when he called him "stupefyingly ignorant".
And he said a no-deal Brexit would not affect the UK's ability to strike a trade deal with the US.
The US president has welcomed Mr Johnson's rise to power, saying he would do a "great job" and even suggesting he was "Britain Trump".
A supporter of Brexit, Mr Trump was critical of former Prime Minister Theresa May's negotiations with the EU.
There have also been tensions over climate change and the US president's views on race and immigration, while a recent row over the leaking of British diplomatic cables led to the resignation of Sir Kim Darroch, the UK's ambassador in Washington.
Woody Johnson told Radio 4's Today his job was to focus on the "things we agree on".
"We're going to have bumps in the road, no question, but we are two great countries," he said.
"If we look forward optimistically between our two countries, we're going to lift all the people in this country - to independence and all the things you voted for in the referendum."
"I think that's what the president wants and what your new prime minister wants too," he added.
In 2015, Boris Johnson, as London Mayor, said Mr Trump's claim that parts of the city were "no-go areas" showed "quite stupefying ignorance" and made him unfit to be president.
But Woody Johnson suggested Mr Trump was not bothered by the comments.
"The new relationship between your new prime minister and our president... it's going to be sensational," he said. "Their leadership has a lot in common. Both have their own style but similarities - a clear vision of what they want to accomplish."
He said the UK would be at the "front of the line" for a trade deal once Brexit had happened and it was "not imperative" for the UK to leave the EU with an agreement to make progress.
"The president is going to try and move the ball forwards - the UK is our most important ally in security and prosperity. He knows that."
Most experts believe a free trade deal with the US will take years to complete and could be beset by difficulties over issues like food standards, environmental regulations and access to healthcare services for each other's companies.
And one of the most powerful politicians in the US has said its Congress would not support any trade agreement which undermined the peace settlement in Northern Ireland.
Nancy Pelosi, Democratic Speaker of the House of Representatives, told the Irish Times there could be no return to physical border checks between Northern Ireland and the Republic of Ireland, something Dublin has said would be inevitable if the UK left without a deal.
"We made it clear in our conversations with senior members of the Conservative Party earlier this year that there should be no return to a hard border on the island," she said.
"That position has not changed. Any trade deal between the US and Great Britain would have to be cognisant of that."
The new prime minister has not yet revealed when he will hold his first face-to-face leaders' meeting with Mr Trump.
No 10 confirmed that Mr Johnson had spoken to the French President Emmanuel Macron over the phone on Thursday and they had discussed Brexit.
A German government spokesperson also said the PM had discussed Brexit with Chancellor Angela Merkel during a phone call on Friday.
"The chancellor has invited the prime minister to visit Berlin for an early first visit," they added.