In a second ceremony at the White House, Justice Anthony M Kennedy, for whom the 49-year-old Mr Gorsuch once served as a clerk, led him through a second oath that justices take, to impartially interpret the laws "and do equal right to the poor and to the rich".
Gorsuch's wife, Louise, and his two daughters were also present at the private constitutional oath ceremony at the court, said Supreme Court spokeswoman Kathy Arberg.
His nomination to a life term marked President Donald Trump's first opportunity to shape for a generation a court that is the ultimate arbiter of numerous most contentious issues in American life.
Gorsuch, previously a Colorado appeals court judge, was confirmed by the Senate last week after a contentious nomination process.
While Republicans and the White House praised Gorsuch as a mainstream and qualified jurist, Democrats sounded the alarm over past rulings that they said reflected a preference for corporate interests.
Democrats accused Mr Gorsuch of being so conservative as to be outside the judicial mainstream, favouring corporate interests over ordinary Americans in legal opinions, and displaying insufficient independence from Trump.
It came only after a bitter month-long fight in Congress that culminated last week with Republican leader Mitch McConnell sweeping aside long-standing Senate rules to win Gorsuch's confirmation by a 54-45 vote.
"Spring is really the ideal backdrop for this joyful gathering of friends, because together we are in the process of reviewing and renewing, and also rebuilding, our country", Trump said.
Read the latest on Donald Trump's first 100 days in office.
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Mostly sunny skies will prevail through mid morning as a high-pressure system remains in control of the local weather pattern. Temperatures will be cooler in the upper 40's with temperatures getting cold Saturday night in the mid 20's.
Gorsuch will take his place as the 113th justice of the Supreme Court.
So where does Gorsuch stand on the spectrum of liberal to conservative, compared with the other active Supreme Court justices?
Gorsuch might provide the key fifth vote on a major case as early as next week.
Gorsuch will soon be hearing and deciding cases involving the Trump administration, including possibly whether to uphold the president's temporary travel ban on people from six majority-Muslim nations.
Petitions from challengers seeking to have their cases heard in the 2017 term that begins in October include a potpourri of contentious issues, including whether concealed guns can be carried in public, whether states can further restrict voting rights, and whether merchants with religious objections can refuse to participate in same-sex marriage ceremonies.
The president also referenced Scalia's legacy, which Gorsuch now is poised to defend, nodding to the late justice's widow, Maureen, who was also in attendance.
The announcement was politically savvy: As Trump struggled to convince conservatives to join his team, the list stood as a promise that he would alter the Supreme Court, should he get the chance.
In most ways, Gorsuch's résumé screams Supreme Court justice: Degrees from Columbia University, Harvard Law School and the University of Oxford. Democrats said they consider the seat "stolen", because Republicans refused to act on President Barack Obama's nominee for the court, Judge Merrick Garland.