In court, Kavanaugh asked questions of both sides in arguments over increased prison sentences for repeat offenders.
Among those who applauded Trump's defense of Kavanaugh was Justice Clarence Thomas, who was confirmed to the court in 1991 following sexual harassment allegations made by Anita Hill, reported The Hill.
The Senate vote approving Kavanaugh's nomination followed a bitter partisan fight that became a firestorm after sexual misconduct allegations emerged.
Kavanaugh took his seat at the end of the bench to Roberts' far left, a visible manifestation of a moment that Republicans have dreamed of for decades, with five solidly conservative justices on the court, and Democrats have dreaded.
Supreme Court Justice Brett Kavanaugh is diving into his new job, asking a handful of questions in the first arguments of the day. But percolating in the courts below are major issues - concerning the Affordable Care Act, DACA and LGBT rights that could be headed to the Supreme Court perhaps as early as this term.
As he departed the White House for a brief trip to Orlando Monday afternoon, Trump lauded Kavanaugh as a "brilliant jurist" and blamed Democrats for the focus on the allegations of sexual misconduct that dominated debate in the weeks before the nominee's Senate confirmation Saturday.
Brett Kavanaugh was sworn in during an official ceremony yesterday at the White House. Kagan, who hired him to teach at Harvard Law when she served as dean, sits next to Kavanaugh.
As Gorsuch did in his first arguments a year ago, Kavanaugh focused heavily on the importance of following earlier decisions of the court.
Trump has repeatedly said that putting conservatives on the court - Kavanaugh is his second appointment - was among the top goals of his presidency.
Kavanaugh's ceremonial swearing-in has some historical precedent, as most of the current members of the Supreme Court had some White House aspect to their oath-takings, even if they already had been done so privately and even started work.
Then, just as his confirmation seemed inevitable, 11th-hour allegations emerged that Kavanaugh sexually assaulted a 15-year-old girl while at high school and exposed himself to a female classmate at an alcohol-fueled dorm party at Yale University.
But Trump, who last week publicly mocked Ford, continued to stoke political divisions at Monday's ceremony, saying Kavanaugh had been the victim of "a campaign of political and personal destruction based on lies and deception".
"I think a lot of Democrats are going to vote Republican", he said.
Mr Kavanaugh is expected to push the court further to the right as he is replacing Justice Kennedy, a conservative who sometimes voted with the liberal justices on key social issues including in cases involving abortion and gay rights.
Both Kavanaugh and Blasey Ford spoke before the Senate Judiciary Committee in an extraordinary day of raw testimony.