Donald Trump has been sworn in as the 47th president of the United States, promising a “revolution of common sense” and taking charge as Republicans assume unified control of Washington and set out to reshape the country’s institutions.

Mr Trump, who overcame impeachments, criminal indictments and two assassination attempts to win another term in the White House, will act swiftly after the ceremony, with executive orders already prepared for his signature to clamp down on border crossings, increase fossil fuel development and end diversity and inclusion programmes across the federal government.

Declaring that government faces a “crisis of trust”, Mr Trump said in his inaugural address that under his administration “our sovereignty will be reclaimed. Our safety will be restored. The scales of justice will be rebalanced”.

President Donald Trump speaks after taking the oath of office during the 60th Presidential Inauguration in the Rotunda of the US Capitol in Washington (Kenny Holston/The New York Times via AP, Pool)

Mr Trump claimed “a mandate to completely and totally reverse a horrible betrayal”, promising to “give the people back their faith, their wealth, their democracy and indeed their freedom”.

He added: “From this moment on, America’s decline is over.”

The executive orders are the first step in what Mr Trump is calling “the complete restoration of America and the revolution of common sense”.

Frigid weather is rewriting the pageantry of the day.

Mr Trump’s swearing-in was moved indoors to the Capitol Rotunda – the first time that has happened in 40 years – and the inaugural parade was replaced by an event at an arena.

Throngs of Trump supporters who descended on the city to watch the inaugural ceremony on the West Front of the Capitol from the National Mall will be left to find somewhere else to view the festivities.

JD Vance and Donald Trump arrive during the 60th Presidential Inauguration in the Rotunda of the US Capitol in Washington (Chip Somodevilla/Pool Photo via AP)

At the Capitol, vice president JD Vance was sworn-in first, taking the oath read by Supreme Court Justice Brett Kavanaugh on a bible given to him by his great-grandmother.

Mr Trump followed moments after noon, using both a family bible and the one used by President Abraham Lincoln at his 1861 inauguration as Chief Justice John Roberts administered his oath.

A cadre of billionaires and tech titans – including Mark Zuckerberg, Jeff Bezos, Tim Cook and Sundar Pichai – were given prominent positions in the Capitol Rotunda, mingling with Mr Trump’s incoming team before the ceremony began.

Guests including Mark Zuckerberg, Jeff Bezos, Sundar Pichai and Elon Musk arrive before the 60th Presidential Inauguration in the Rotunda of the US Capitol in Washington (Julia Demaree Nikhinson, Pool/AP)

Also there was Elon Musk, the world’s richest man, who is expected to lead an effort to slash spending and federal employees.

Mr Trump began the day with a prayer service at St John’s Episcopal Church.

He and his wife, Melania, were later greeted at the North Portico of the executive mansion by outgoing President Joe Biden and first lady Jill Biden for the customary tea and coffee reception.

It was a stark departure from four years ago, when Mr Trump refused to acknowledge Mr Biden’s victory or attend his inauguration.

“Welcome home,” Mr Biden said to Mr Trump after the president-elect stepped out of the car.

President Joe Biden, centre left, and first lady Jill Biden, left, pose with President-elect Donald Trump, centre right, and Melania Trump, right, upon arriving at the White House in Washington (Evan Vucci/AP)

The two presidents, who have spent years bitterly criticising each other, shared a limo on the way to the Capitol.