Mr. Trump and his wife Melania were greeted in the Saudi capital by King Salman on Saturday morning local time.
The eight-day trip will also take in Israel, the Palestinian territories, Brussels, the Vatican, and Sicily.
The visit comes as Mr. Trump faces uproar at home following his sacking of FBI director James Comey.
He has strongly criticized the decision to appoint a special counsel to oversee an inquiry into alleged Russian influence on the US election.
Mr. Trump is accompanied on his visit by his daughter Ivanka, an unpaid White House adviser, and her husband Jared Kushner, a key member of the Trump cabinet.
Like British Prime Minister Theresa May and German Chancellor Angela Merkel on their recent visits to Saudi Arabia, Mrs. Trump and Ivanka Trump did not wear headscarves.
In January 2015, Mr. Trump criticized then-First Lady Michelle Obama for doing the same. In a tweet, Mr. Trump said she had "insulted" her hosts.