Mr Kavanaugh was officially sworn in at a White House event after US Senate hearings in which he denied allegations of sexual assault against him.
“On behalf of our nation, I want to apologize to Brett and the entire Kavanaugh family for the terrible pain and suffering you have been forced to endure,” Mr Trump said.
With all the sitting justices in attendance, along with Mr Kavanaugh’s family and top administration officials, Mr Trump said Mr Kavanaugh had been the victim of a “campaign of political and personal destruction based on lies and deception”.
But, he told the new justice, “You, sir, under historic scrutiny, were proven innocent.”
Mr Kavanaugh officially became a member of the high court on Saturday and has already been at work preparing for his first day on the bench on Tuesday.
In his own remarks, Mr Kavanaugh, who has faced criticism that he appeared too politicised in his Senate testimony, tried to assure the American public that he would approach the job fairly.
He said the high court “is not a partisan or political institution” and assured he took the job with “no bitterness”.
“The Senate confirmation process was contentious and emotional. That process is over. My focus now is to be the best justice I can be,” he said.
It was the end of a deeply contentious nomination process that sparked mass protests, an FBI investigation and it comes less than a month before pivotal midterm elections that will determine which party controls Congress.
Ceremonial swearing-ins are unusual for new justices. Only Samuel Alito and Stephen Breyer participated in White House events after they had been sworn in and begun work as justices, according to the court’s records on the current crop of justices.
Mr Kavanaugh and his law clerks already have been at the Supreme Court preparing for his first day on the bench on Tuesday, when the justices will hear arguments in two cases about longer prison terms for repeat offenders.
The new justice’s four clerks all are women, the first time that has happened.
The clerks are Kim Jackson, who previously worked for Mr Kavanaugh on the federal appeals court in Washington, Shannon Grammel, Megan Lacy and Sara Nommensen.
The latter three all worked for other Republican-nominated judges. Ms Lacy had been working at the White House in support of Mr Kavanaugh’s nomination.