If confirmed by the Senate, the 49-year old would restore the court’s conservative majority, lost together with the passing of Justice Antonin Scalia.
The court gets the final legal word on several of the very sensitive US problems, from abortion to sex to gun control.
Mr Trump said Judge Gorsuch had a “brilliant mind, an unparalleled legal education, as well as a dedication to interpreting the Constitution based on text”.
“Judge Gorsuch has excellent legal abilities, a brilliant thoughts, incredible discipline, and has earned bipartisan support,” Mr Trump said.
He was decided from a shortlist of 21 selections, which Mr Trump made public through the election campaign.
He said: “”It’s the job of judges to apply, not change, the work of the people’s representatives. A judge who enjoys every result he reaches is quite likely a poor judge, elongating for results he favors rather than those the law demands.”
Judge Gorsuch is a so called originalist, meaning he considers the US Constitution needs to be followed as the Founding Fathers thought.
Demonstrations against Mr Trump’s selection were held outside the Supreme Court after the statement.