"I think they do have a lot (in common). Both these leaders have their own style, but they have similarities and I think they have clear vision of what they want to accomplish," the ambassador told the BBC.
Trump had welcomed Boris Johnson's rise to power earlier this week, saying he would do a "great job" and even described him as "Britain Trump".
"We have a really good man who's going to be the Prime Minister of the UK now," the US President had said. "He's tough and he's smart. They're saying 'Britain Trump'. They call him 'Britain Trump' and people are saying that's a good thing."
The ambassador played down Boris Johnson's criticism of Trump when he was London Mayor. That time, he had called the then US presidential candidate "stupefyingly ignorant".
Woody Johnson said he was sure the US President was aware of the comments. "Donald Trump is going to say what he wants to say when he wants to say it and he will comment on injustices or inabilities or how he sees it. I think he respects Boris for the same. Boris is going to call it as he sees it."
"But first of all I don't think it's long-lasting and second of all I think they have so much more in common in terms of what they want to accomplish for the good of both of our nations."
The ambassador said a no-deal Brexit would not affect the UK's ability to strike a trade deal with the US.
According to him, Britain would be at the "front of the line" for a trade deal once Brexit happens and it is "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," said Woody Johnson.
The new UK Prime Minister has not yet revealed when he will hold his first face-to-face leaders' meeting with Trump.
No 10 confirmed that Boris Johnson had spoken to the French President Emmanuel Macron over the phone on Thursday and they had discussed Brexit.
( With inputs from IANS )