Nicola Sturgeon congratulated President Biden and Vice President Kamala Harris shortly after they were sworn in.
Scotland’s First Minister tweeted: “Warm congratulations and best wishes to President Biden and Vice President Harris. Scotland and the USA share long-standing bonds of friendship and co-operation.
“We look forward to building on these in the years ahead.”
Boris Johnson also welcomed Biden’s succession from Donald Trump as a “step forward” from a “bumpy period” and an opportunity to collaborate on climate change and the coronavirus pandemic, two crises the Republican played down.
Mr Biden declared “democracy has prevailed” as he took over the White House after four years of a Republican presidency that tested the nation’s tenets as well as international relations.
“This is America’s day. This is democracy’s day. A day in history and hope, of renewal and resolve,” the Democrat said.
But he noted that “the world is watching” as he took the oath of office in Capitol Hill, the scene of a violent insurrection from Trump loyalists just two weeks ago.
“Here’s my message to those beyond our borders. America has been tested and we’ve come out stronger for it. We will repair our alliances and engage with the world once again, not to meet yesterday’s challenges but today’s and tomorrow’s challenges,” Mr Biden said.
“And will lead not merely by example of our power but by the power of our example. We will be a strong and trusted partner for peace, progress and security.”
At 78, Mr Biden became the oldest president to take office but in a more significant moment of history making, Kamala Harris was sworn in as vice president.
She is the first woman to become vice president, as well as the first black person and the first person of South Asian descent to serve in the role.
The Prime Minister, who had a close but at times strained relationship with Mr Trump, tweeted his “congratulations” to Mr Biden on being sworn in as well as to Ms Harris “on her historic inauguration”.
“When you look at the issues that unite me and Joe Biden, the UK and the United States right now, there’s a fantastic joint common agenda,” Mr Johnson added to reporters.
“It’s a fantastic thing for America, a step forward for the country that has been through a bumpy period.
“And for us and America it’s a big moment.”
Mr Johnson has said he looks forward to welcoming Mr Biden this year to the G7 summit in Cornwall and the Cop26 climate change conference in Glasgow.
Mr Biden will on his first day issue a series of executive actions as he begins overturning some of his predecessor’s legacy.
In actions that will be welcomed by Mr Johnson, the president will rejoin the Paris Climate Accord and the World Health Organisation.
Taking the helm of the nation with the highest Covid-19 death toll in the world, Mr Biden accepted the scale of the challenge ahead of him after what he described as a “winter of peril”.
He called on Americans to “end this uncivil war” that exploited divisions, declaring that “unity is the path forward”.