He emphatically denied the allegations. It was the narrowest Senate vote to confirm a justice since 1881.
Chief Justice John Roberts welcomed Kavanaugh on behalf of the entire court, wishing him the traditional "long and happy career in our common calling".
At a White House ceremony on Monday night, Kavanaugh said he was starting his new job without bitterness.
"Far left activists decided that the United States Senate and their members should be harassed and intimidated wherever they might be".
After an extra Federal Bureau of Investigation probe - which media reports say was drastically curtailed by the White House - also found nothing new, Kavanaugh was finally voted into the coveted post.
"Those who step forward to serve our country deserve a fair and dignified evaluation, not a campaign of political and personal destruction based on lies and deception", Trump said in the East Room of the White House.
Trump is apologizing to Kavanaugh and his family for "the awful suffering you have been forced to endure".
Trump continued: "And with that I must state that you, sir, under historic scrutiny, were proven innocent". A yawning divide has opened in the past year over whether allegations of sexual misconduct should be enough to topple accused men from the pinnacle of their professions.
And on Monday evening he was the guest of honor at a ceremonial swearing-in at the White House.
China tells Pompeo US must stop 'misguided actions'
The US has imposed tariffs on virtually half of all Chinese imports into the US and has threatened to target all of its imports. China's foreign minister argued the U.S.is responsible for escalating trade conflicts.
Kavanaugh was quick to weigh in, asking his first question of a lawyer representing a defendant about 20 minutes into the first argument.
On Wednesday, the only other day of arguments this week, the court will hear another two hours of arguments. The event is unusual for new justices. He will take notes for the justices when they meet for private conferences.
The high court now has five conservative justices and four liberals. The new justice's four clerks all are women, the first time that has happened. The latter three all worked for other Republican-nominated judges.
Kavanaugh seemed aware of the cloud that hung over his ascension to the nation's highest court and attempted to downplay the partisan tensions that burned during the Senate's consideration of his nomination.
"The Supreme Court is a team of nine. That is who I am".
Protesters and demonstrations necessitated "extraordinary security measures" to protect the Senate, Supreme Court, the Kavanaugh family, he said. "The best student, the best scholar, the great intellect, incredible record over many years". False charges. False accusations.
He called the Kavanaugh row "a disgraceful situation brought about by people who are evil", and said that the result was "very exciting". And he toughed it out. In 1967, Thurgood Marshall became the first African-American Justice; Clarence Thomas became the second in 1991.
His ascent to the court was sealed by a 50-48 Senate vote last Saturday. It capped a fight that seized the national conversation after claims emerged that Kavanaugh had sexually assaulted women three decades ago.