Legal experts break down what Kennedy's retirement could mean for the high court and the Sacramento native's impact.
The judge, 81, will retire on 31 July.
At one point, Trump praised Kennedy for his service and said he was "honored" that the longtime justice chose to retire during his presidency - which he suggested was a deliberate choice.
President Trump said that he found out about Kennedy's retirement a half-hour before it was announced - he had in fact gone to the White House to talk to the president for about 30 minutes, and Kennedy offered recommendations about who might replace him, the president told reporters during a meeting with the president of Portugal. "It's one of most important things we can do". The judge's retirement gives Mr Trump his second Supreme Court pick since he became president, and he has said he will choose from a list of 25 conservative candidates. Republicans changed the rules during Gorsuch's confirmation to wipe out the main delaying tactic for Supreme Court nominees, the filibuster, and the need for 60 votes to defeat it.
Of his travel ban, which prohibits visitors and immigrants from five Muslim-majority countries, along with North Korea and Venezuela, Trump called it a "common-sense policy to improve vetting and national security".
Another live issue expected to come back to the court is whether people who run businesses can refuse service to gay couples because of religious objections to same-sex marriage.
"It is probably the biggest legacy that this president will have and one of the untold success stories so far", Spicer said during an interview on "The Intelligence Report" on Wednesday.
Trump added that his nominee to fill the Supreme Court's vacancy will be on the bench for 40 to 45 years.
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"The significance of today's news can not be overstated: The right to access abortion in this country is on the line", said Dawn Laguens, the group's executive vice president.
"If we put another two or perhaps three justices on, that is really what will happen. Because I am putting pro-life justices on the court", Mr Trump said during an October 2016 debate with Hillary Clinton.
Republicans now hold a bare 51-49 majority in the Senate, although that includes the ailing Sen.
A person familiar with the White House selection process said 53-year-old Kavanaugh is at or near the top of Trump's list of possible nominees.
"Anything but that would be the absolute height of hypocrisy".
Kennedy was nominated in 1987 by President Reagan to the court, after Robert Bork's nomination failed and Douglas Ginsburg was pressured to withdraw after questions were raised about his admission he had smoked marijuana several times. A Republican appointee, he has held the key vote on such high-profile issues as abortion, affirmative action, gay rights, guns, campaign finance and voting rights.
Senate Minority Leader Chuck Schumer says it would be the "height of hypocrisy" for the Senate to vote on a new Supreme Court justice before the November midterm elections.
"During his tenure on the Court, he authored landmark opinions in every significant area of constitutional law, most notably on equal protection under the law, the separation of powers, and the First Amendment's guarantees of freedom of speech and religion", the White House said in a statement.