After POTUS was finished torching Democrats and Ford, Kavanaugh spoke of being a "force for stability and unity".
Trump has repeatedly said that putting conservatives on the court - Kavanaugh is his second appointment - was among the top goals of his presidency.
Speaking later on Monday afternoon Trump amplified his views about Kavanaugh's treatment by Democrats during the confirmation fight, when he gave a speech in Orlando, Florida before the International Association of Police Chiefs.
The president - whose Republicans fear losing at least the lower chamber of Congress - predicted that Democrats would pay for their attempts to block the confirmation, especially during the lurid debate over decades-old sexual assault allegations. Only one Democrat voted for Trump's nominee.
The new justice is widely expected to push the court further to the right as he is replacing Kennedy, a conservative who sometimes voted with the liberal justices on key social issues, including in pivotal cases on gay rights. In so doing, Trump apologized to Kavanaugh "on behalf of our nation", for the "terrible pain and suffering" he has been "forced to endure" at the hands of the opposition's alleged campaign of "personal destruction based on lies and deception".
"Every American can be assured that I will be an independent and impartial justice", Kavanaugh said in the White House East Room after a ceremonial swearing-in.
He then announced, "You sir, under historic scrutiny, were proven innocent" before giving the new justice a handshake. Almost two-thirds, or 63%, of likely women voters said they will vote for the Democratic congressional nominee in November, compared to 33% of likely women voters who said they'll vote Republican.
"What happened to the Kavanaugh family violates every notion of fairness, decency and due process", the president said in his remarks at the swearing in.
Kavanaugh also announced that all four of his law clerks will be women - "a first in the history of the Supreme Court".
The judge was confirmed by the Senate on Saturday, in a 50-48 vote that largely followed partisan lines.
Kavanaugh's elevation to the high court had been considered safe until California university professor Christine Blasey Ford went public with explosive allegations that Kavanaugh had sexually assaulted her in 1982, while they were in high school. However, the Republican cautioned that "it remains to be seen whether this lasts for the next three weeks or not". He took his oaths of office in a private ceremony at the Supreme Court on Saturday evening.
Samuel Chase in 1804 was the only justice to be impeached by the House. The court will be hearing arguments in two previously little-noticed cases involving the Armed Career Criminal Act, a federal law that imposes heightened penalties on people who repeatedly commit serious crimes.
Many observers have noted that Kavanaugh's confirmation itself represent a triumph of minority rule, in two senses.