The Senate acquitted Mr Trump of incitement to insurrection following the storming of Congress on 6 January.
Mr Johnson told US broadcaster CBS his relationship with new President Joe Biden was "excellent".
And he promised the American and UK governments would work well together on issues like climate change and defence.
Mr Biden, who was inaugurated on 20 January, has never met the prime minister in person, but this is set to change later this year, with the UK hosting the G7 summit in the summer and the COP26 climate change gathering in the autumn.
During his interview for CBS's Face the Nation show, Mr Johnson was keen to stress that their two countries were "coming together" on the environment, ways of dealing with Iran and the future of Nato.
These were all issues on which Mr Trump took a different line to the UK government, but the prime minister called recent statements by Mr Biden "incredibly encouraging".
Having previously condemned the violence inside Washington's Capitol building last month, he was asked about the impeachment trial of Mr Trump, in which prosecutors failed to get the two-thirds majority in the Senate needed to convict the ex-president.
"I think the clear message that we get from the proceedings in America is that, after all the toings and froings and all the kerfuffle, American democracy is strong," he said.
"And the American constitution is strong and robust. And we're delighted now, I'm very delighted, to have a good relationship with the White House, which is an important part of any UK prime minister's mission.
"I've had some good conversations already with President Biden, fantastic conversations about the way he sees things."
Five people died in the violence in Washington on 6 January.
Earlier on Sunday, Mr Biden described democracy - in contrast to Mr Johnson - as "fragile" in the face of "violence and extremism".
He said of Mr Trump's trial: "While the final vote did not lead to a conviction, the substance of the charge is not in dispute."
But Mr Trump welcomed his acquittal, calling his impeachment a "witch hunt".
In his first telephone call to the prime minister last month, Mr Biden said he wanted to "strengthen the special relationship" between the US and UK.