The American firebrand held a speech to praise his nominee, whom he described as a “fair-minded, unbiased and even-handed person”.
Judge Kavanaugh has been embroiled in a fierce row over historic allegations of sexual misconduct, which he denies.
Trump reminded the audience that “after historic scrutiny”, Mr Kavanaugh was proven innocent.
He also apologised to the conservative judge and his family “on behalf of the nation” for the “campaign of political and personal destruction” he faced during his confirmation process.
The US President claimed it violated “every notion of fairness, decency, and due process”.
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After being announced on stage, Mr Kavanaugh thanked President Trump “for everything”.
He also acknowledged the partisan rancour that surrounded his confirmation.
He said: “All nine of us revere the Constitution.
“The Supreme Court is an institution of law.
“It is not a partisan or political institution.
“The justices do not sit on opposite sides of the aisle.
“The Supreme Court is a team of nine, and I will always be a team player on the team of nine.”
Standing in front of his wife and two daughters, Mr Kavanaugh noted how the confirmation process was a contentious and emotional ordeal, but added: “I take this office with gratitude and no bitterness.”
The conservative judge vowed to be “impartial” and claimed he “was not appointed to serve one party or one interest, but to serve one nation”.
Mr Kavanaugh already took his official oaths during a private ceremony at the Supreme Court on Saturday.
The US Senate, controlled by the Republican Party, confirmed his appointment to the Supreme Court by 50 votes to 48.
Nevertheless, the US President decided to hold ceremonial swearing-in ceremony for him at the White House, as he continues to celebrate the successful confirmation of his second Supreme Court nominee in less than two years.