The Republican Party has won a majority in the US House of Representatives, American media projected on Wednesday, completing their clean sweep of Congress and handing President-elect Donald Trump vast legislative power.

After more than a week of vote counting, CNN and NBC projected that the Republicans had reached the 218 seats needed to retain their majority in the 435-seat lower chamber, having already secured control over the Senate.

"It is a beautiful morning in Washington. It is a new day in America," said House Speaker Mike Johnson, who held a press conference to celebrate victory before the result was official.

"The sun is shining, and that's a reflection about how we all feel. This is a very, very important moment for the country and we do not take it lightly."

Trump triumphed in each of the seven battleground states in the November 5 presidential election and also won the national popular vote, with preliminary figures showing him ahead of Democratic Party challenger Kamala Harris by 3.2 million votes.

Having control of both chambers of Congress will clear the way for him to confirm his nominations for key positions in his administration and will also allow him to push through his radical agenda of mass deportations, tax cuts and slashing regulations.