Congress certified Mr Biden's 306 votes to Mr Trump's 232 after rejecting two objections to the tally.
It comes after a mob stormed the US Capitol on Wednesday in an attempt to overturn November's election result.
In a statement, Mr Trump finally accepted defeat and said there would be an "orderly transition" on January 20.
He said: “Even though I totally disagree with the outcome of the election, and the facts bear me out, nevertheless there will be an orderly transition on January 20.
"I have always said we would continue our fight to ensure that only legal votes were counted.Insurance Loans Mortgage Attorney Credit Lawyer
"While this represents the end of the greatest first term in presidential history, it’s only the beginning of our fight to Make America Great Again!”
Protesters clashed with police in violent scenes in Washington DC.
One woman died after being shot inside the Capitol, while three others died after suffering "medical emergencies", according to police chief Robert Contee.
Demonstrators forced their way into the building after a rally was held near the White House where Mr Trump encouraged them to march on Capitol Hill.
Mr Trump previously urged his supporters to travel to Washington to protest against Congress' approval of Mr Biden's presidential election victory.
As protesters attacked the Capitol, both chambers of