The Senate earlier backed his nomination by 50 votes to 48, BBC reported on Saturday.
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 Trump a political victory ahead of key mid-term elections in November.
Ahead of the vote, hundreds of people protested against Kavanaugh’s nomination at the US Capitol in Washington.
During the vote, other protesters shouted “shame” from the public gallery and Vice-President Mike Pence had to call for order to be restored.
Kavanaugh’s appointment is for life and he will strengthen conservative control of the nine-judge court, which has the final say on US law.
The 53-year-old was sworn in on Saturday evening in a private ceremony at the Supreme Court. Chief Justice John Roberts administered the constitutional oath and retired justice Anthony Kennedy — whom Kavanaugh is replacing — administered the judicial oath.
Protesters had gathered outside the court and at one point some ran up the steps and banged on its ornate doors. Other demonstrators climbed on the nearby statue of justice.
“I applaud and congratulate the US Senate for confirming our GREAT NOMINEE, Judge Brett Kavanaugh, to the United States Supreme Court. Later today, I will sign his Commission of Appointment, and he will be officially sworn in. Very exciting!” Trump tweeted.
Later, he spoke to reporters aboard Air Force One, saying Kavanaugh had withstood a “horrible attack by the Democrats” and that women were “outraged” at what had happened to the nominee.
Trump also said he was “100 per cent certain” that the woman who had accused Kavanaugh of sexual assault, Christine Blasey Ford, had named the wrong person.
The upper house is split 51-49 in favour of the Republicans and the vote was largely along party lines. In the end, there was indeed a two-vote margin, the closest nomination vote since 1881.
The only party dissenters were Republican Senator Lisa Murkowski, who had intended to vote no, and Democrat Joe Manchin, who voted yes.
That should have meant a 51-49 tally, but the absence of Republican Steve Daines, a yes voter who was at his daughter’s wedding, altered the final figures.
Murkowski opted instead to simply mark herself as “present”, leaving the final vote 50-48.