The Senate vote takes the highest US court down a more conservative path for perhaps a generation and is a bitter blow to Democrats already chafing at Republican control of the White House and both chambers of the US Congress.
Mr Trump also said he was "100% certain" that the woman who had accused Mr Kavanaugh of sexual assault, Christine Blasey Ford, had named the wrong person.
The Senate backed Brett Kavanaugh's nomination by 50 votes to 48.
Democratic senators, who had battled hard to block the 53-year-old judge, insisted the caustic battle over Kavanaugh would galvanize Democrats at the polls. Chief Justice John Roberts administered the Constitutional oath, and retired Justice Anthony Kennedy administered the judicial oath, according to a Supreme Court statement, "so that [Kavanaugh] can begin to participate in the work of the court immediately".
Trump spoke to reporters on the White House lawn.
"This has all really helped me: No. 1, unify my conference and No. 2, underscore the significance of the Senate", the Kentucky Republican said.
With tensions simmering, Pence got an earful from activists who booed and chanted "Vote them out!" as he walked to his motorcade.
Protesters swarmed the streets of Washington, and rushed to the steps of the Supreme Court to.
Kavanaugh's confirmation process has laid bare the partisan gridlock on Capitol Hill and the political polarization of America just a month before midterm elections. "The democrats have become too extreme and too risky to govern", Trump said.
'These uncorroborated accusations have been unequivocally and repeatedly rejected by Judge Kavanaugh, and neither the Judiciary Committee nor the Federal Bureau of Investigation could locate any third parties who can attest to any of the allegations, ' Grassley said.
Jim Risch, a Republican from Idaho, agreed, saying the friendships that cross party lines are genuine.
"We need healing", Murkowski told reporters afterwards.
As he did during his confirmation hearing, Kavanaugh also told Collins that Roe v. Wade, which was affirmed by the Supreme Court in a 1992 case, is "a precedent on a precedent".
His ascent to the Supreme Court was thrown into doubt last week after university research psychologist Christine Blasey Ford testified that he had sexually assaulted her at a Washington area gathering in the early 1980s.
Sen. Chris Coons, Delaware Democrat, described talk of impeaching the newly sworn-in justice "premature", and called instead for concentrating on the November election.
The moderate Republican senator sat down for a 60 Minutes interview with longtime CBS anchor, Scott Pelley, whom she discussed the matter into further detail with. "But what you just said now was it's a question of whether or not the party in control of the Senate is different than the president". "The country is badly polarised, and they elect people to represent them here who have the same point of view that they do", he said recently.