Neil Gorusch's nomination is seen as a move by President Donald Trump to restore the Supreme Court's conservative majority and help shape rulings on divisive issues such as abortion, gun control, the death penalty and religious rights.
He is expected to fill the vacancy created by the death of conservative justice Antonin Scalia in February last year.
In an announcement at the White House, Mr Trump said the move was part of a pre-election promise.
"Months ago, as a candidate, I publicly presented a list of brilliant and accomplished people to the American electorate and pledged to make my choice from among that list. Millions of voters said this was the single most important issue to them when they voted for me for president. I am a man of my word, I will do as I say - something that the American people have been asking for from Washington for a very, very long time."
At 49 years of age Neil Gorsuch is the youngest Supreme Court nominee since Republican President George W. Bush picked 43-year-old Clarence Thomas in 1991.
He is currently serving as a judge on the 10th Circuit Court of Appeals in Denver, Colorado.
It's the city of his birth and where he was appointed to the post in 2006 by President Bush.
He told reporters he is honoured to have been selected.
"The towering judges that have served in this particular seat of the Supreme Court, including Antonin Scalia and Robert Jackson, are much in my mind at this moment. Justice Scalia was a lion of the law. Agree or disagree with him, all of his colleagues on the bench cherished his wisdom and his humour and, like them, I miss him."
Judge Gorsuch is known for his strong conservative views, including on euthanasia.
His nomination immediately provoked both praise and condemnation.
A group of Evangelical Christians gathered outside the Supreme Court in Washington to offer what they said was the first prayer for him.
Katherine Glenn-Foster from the 'pro-life' Sound Legal Group welcomed the news.
"We are delighted that he is a proven originalist, a textualist and a jurist in the mold of Justice Scalia. He is the perfect replacement. He is the perfect replacement to fill Justice Scalia's chair. We pray here tonight that the nomination process would go smoothly, that Judge Gorsuch would be seated and that he will continue to respect the Constitution and protect life, religious liberty and the other tenets on which our nation was founded. Thank you."
The Leadership Conference on Civil and Human Rights was among those opposing Judge Gorsuch's selection.
Wade Henderson is the group's president.
"We are here tonight to demand not to ask, to demand that the independence of our United States Supreme Court be protected from being mangled and mauled by someone whose administration does not appear, I admit it's early, but it doesn't appear to be committed to protecting the Constitutional rights of all of us and we won't accept anything less."
Democrats are likely to oppose his appointment during the confirmation hearing in the Senate.
President Trump had the chance to nominate Judge Gorsuch because last year the Republicans refused to consider Merrick Garland, the former Democratic President Barack Obama's nominee.
