The Republican-controlled Senate held a rare New Year's Day session to debate the move, which had already been voted for by the House of Representatives.

The $740bn bill will fund defence policy for the year to come.

Mr Trump, who leaves office in a few weeks, objected to certain provisions in the bill.

The Senate voted 81-13 for the National Defense Authorization Act (NDAA) - a two-thirds majority is required to override a presidential veto in both chambers.

It comes just two days before a new US Congress is due to be sworn in.

Mr Trump had taken issue with policies that limit troop withdrawals from Afghanistan and Europe and remove Confederate leaders' names from military bases.

He also wanted the bill to repeal a liability shield for social media companies.

Before the debate began, Senate Republican leader Mitch McConnell said he was determined to pass the bill.

"Here's what the Senate is focused on - completing the annual defence legislation that looks after our brave men and women who volunteer to wear the uniform.

"We've passed this legislation 59 years in a row. And one way or another, we're going to complete the 60th annual NDAA and pass it into law before this Congress concludes on Sunday," he added.