At 81, Kennedy is the second-oldest justice. He will retire on July 31 just after his birthday next month.
Kennedy joined the court in 1988 after being appointed by Republican President Ronald Reagan.
He cast swing votes in cases on gay rights, healthcare and political spending.
Trump touched on the importance of his choice to replace him in an Oval Office meeting the Portuguese president.
'I think we can all say one of the most important events. One of the most important things for our country,' he said. 'It's always been considered a tremendously important thing.'
Republicans hold 51 seats in the chambers that has authority to approve the president's appointments. They lowered the threshold for court appointments last year in order to push through Gorsuch.
The president said he will begin searching for a replacement immediately who will 'hopefully be as outstanding.'
'I know that he will be around hopefully for a long time to advise,' he said of Kennedy.
The retiring justice, he revealed, will be 'teaching and doing a lot of things.'
Trump said that he met with Kennedy for a half-hour earlier today before he made the public announcement.
An official White House statement said: 'Today, we thank Justice Anthony M. Kennedy for his thirty years of distinguished service on the Supreme Court of the United States. In 1987, President Reagan nominated him to the Court, and he was swiftly confirmed without opposition. A Californian—like the President who appointed him—Justice Kennedy is a true man of letters. 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.
'Justice Kennedy has been a tireless voice for individual rights and the Founders’ enduring vision of limited government. His words have left an indelible mark not only on this generation, but on the fabric of American history.
Trump told reporters he'd be picking a replacement off of an already-culled White House list.
'We have obviously, a number of people, 25 people,' he said, noting he had 20 in the general election and has since added five.
'We have a very excellent list,' he said of 'highly-educated' people who he said are also very talented.
'I think you see the kind of quality that we're looking at when you see that list. '
Kennedy was confirmed by a unanimous Senate vote during Ronald Reagan's final year in office and was known as a 'swing vote,' arbitrating 5-4 decisions that pitted conservative justices against liberal ones.
Asked in 2015 if he relished the power that came with that role, he demurred: 'I think that's overrated.'
He had plenty of spotlight moments that made Republicans wonder whether Reagan had chosen wisely.
Just four years after joining the Court, Kennedy co-authored a decision in 'Planned Parenthood v. Casey,' which upheld the 'Roe v. Wade' decision legalizing abortion.
But in 2007 he swung in the other direction, voting with conservatives in a 5-4 split on 'Gonzales v. Carhart,' upholding a nationwide ban on partial-birth abortions.
In George W. Bush's last year as president, Kennedy wrote a 5-4 majority opinion declaring that the U.S. Constitution guaranteed 'habeas corpus' rights to inmates at the Guantanamo Bay military prison.
During President Barack Obama's second term in office, Kennedy's judgment trended further to the left.
He wrote the 2012 majority opinion in 'Arizona v. United States,' which overturned three sections of Arizona's controversial 2010 immigration law.
One provision that the Supreme Court axed had authorized warrantless arrests of illegal immigrants whom state officials thought were eligible for deportation.
A year later he wrote a majority opinion striking down part of the Defense of Marriage Act.
In 'United States v. Windsor,' a 5-4 vote established that DOMA, which defines a marriage as a 'legal union between one man and one woman,' denied same-sex couples their Fifth Amendment rights to equal protection under federal law.
In 2015 Kennedy struck the final blow for same-sex marriage, again serving as a swing vote in a 5-4 decision.
In 'Obergefell v. Hodges,' he wrote the opinion making it legal in all 50 states for gays and lesbians to marry.
Researchers at SCOTUSblog have documented how Kennedy's swing-vote status helped the conservative wing of the Court during his early years, a state of affairs that changed as he swung to the left more recently.
Between 2010 and 2014, America's highest court issued 57 decisions that hung on razor-thin 5-4 margins
Of those, Kennedy sided with conservatives 37 and liberals 20 times.
But from 2015 to 2017, there were 23 different close-shave decisions; Kennedy pleased the left in 15 of those cases, and voted with the right only 8 times.
