Video report by ITV News Washington Correspondent Robert Moore
Speaking a day ahead of President-elect Joe Biden’s inauguration, the outgoing president said "political violence is an attack on everything we cherish as Americans."
He added: "It can never be tolerated".
President Trump initially refused to the condemn the violence of Trump supporters who stormed the Capitol on January 6, telling them in a video posted on the day: "We love you".
He has since hardened his stance, calling on protesters to remain peaceful ahead of Mr Biden's inauguration.
But many hold President Trump responsible for the riots - blaming his false claims of voter fraud, and a speech he gave ahead of the insurrection, for the violence.
In the message posted by the White House on YouTube - with Mr Trump temporarily banned from the site - the outgoing president said he would pray for the success of the next administration.
"This week, we inaugurate a new administration and pray for its success in keeping America safe and prosperous," Mr Trump said.
Breaking with tradition, the outgoing president has refused to attend the inauguration.
Washington DC is on high alert ahead of the event, with hundreds of troops patrolling the city amid heightened security procedures in light of the storming of the Capitol.
But Mr Trump at no point mentioned his successor by name in his farewell address.
In the nearly 20-minute speech taped in the White House Blue Room, the outgoing president only referred to the "next" and "new" administration.
In the address, Mr Trump also praised himself on what he was most "proud" of during his time in office.
He cited efforts to normalise relations in the Middle East, adding: "I am especially proud to be the first president in decades who has started no new wars."
On his next moves after leaving office, Mr Trump said: "I want you to know that the movement we started is only just beginning".
"We did what we came here to do - and so much more."
Mr Trump's farewell address came as the US reached the grim milestone of 400,000 Covid-19 deaths on Tuesday.