The nomination of Gorsuch, a 49-year-old federal appellate judge from Colorado, gives Trump and Republicans the opportunity to confirm someone who could cement the conservative direction of the court for decades.
His selection also sets up an intense fight with Senate Democrats, still angry over the Republicans' decision to essentially ignore former President Barack Obama's nomination of Judge Merrick Garland for the empty Supreme Court seat last year.
Trump made the announcement after an unusual day in which both top candidates for the nomination -- Gorsuch and Judge Thomas Hardiman -- were brought to Washington as the suspense built.
The court has been operating with eight justices since the sudden death last February of Justice Antonin Scalia. If confirmed, Gorsuch would continue the ideological balance that existed before Scalia's death, with four conservatives, four liberals and Justice Anthony Kennedy as a swing vote between the blocs.
Trump selected Gorsuch -- who sits on the 10th Circuit Court of Appeals -- from a list of 20 potential justices compiled during the presidential campaign in a direct appeal to conservative and evangelical voters skeptical about his commitment to their values.
Gorsuch's opinions on religious liberty, where he sided with the challengers to the so-called Obamacare contraceptive mandate, and on the separation of powers, where he said too much deference was given by the courts to administrative agencies, are key to his appeal to Republicans. As is his age. At 49, he could carry on Trump's legacy long after the President leaves office.
CNN's George Phillips contributed to this report.
By Ariane de Vogue CNN Supreme Court Reporter
U.S. Senator Roy Blunt (Mo.) released the following statement:
“Judge Neil Gorsuch is a well-respected jurist with the experience and qualifications to serve on our nation’s highest court. In his decade on the 10th U.S. Circuit Court of Appeals bench, he has demonstrated a steadfast commitment to upholding the rule of law and interpreting the Constitution as its authors intended. The Supreme Court is one of the most important legacies this president is likely to leave, and he made the right choice in selecting Judge Gorsuch to begin shaping the long-term view of the court. I look forward to hearing more from Judge Gorsuch as the confirmation process moves forward.”