The Senate earlier backed his nomination by 50 votes to 48.
Mr Kavanaugh had been embroiled in a bitter battle to stave off claims of sexual assault, which he denies.
But after an 11th-hour investigation by the FBI into the allegations, enough wavering senators decided to support the nomination.
His confirmation hands Mr Trump a political victory ahead of key mid-term elections in November.
Ahead of the vote, hundreds of people protested against Mr Kavanaugh's nomination at the US Capitol in Washington.