The US president, who upset many Muslims by attempting to ban travellers from seven countries where the religion is prevalent, will travel to the Middle East later this month.
Israel will be his second stop before he is received by the Pope at the Vatican on 24 May.
Speaking in the Rose Garden at the White House, Mr Trump said: “My first foreign trip as president of the United States will be to Saudi Arabia, then Israel, and then to a place that my cardinals love very much, Rome.
“Saudi Arabia is the custodian of the two holiest sites in Islam.
“It is there we will begin to construct a new foundation of cooperation and support with our Muslim allies to combat extremism, terrorism and violence and to embrace a more just and hopeful future for young Muslims in their countries.”
White House officials said Mr Trump will aim to show his “America first” policy is compatible with the US being a global leader.
He expects the trip to produce “tangible results” in the fight against Islamic State, they added.
Mr Trump’s visit to Israel follows his meeting with Palestinian leader Mahmoud Abbas at the White House on Wednesday, when he pledged to end one of the world’s oldest conflicts.
“It is something that I think is, frankly, maybe not as difficult as people have thought over the years,” said Mr Trump.
The US president will meet the Pope ahead of the G7 summit in Sicily at the end of May.
Mr Trump clashed with the Pontiff while campaigning to become the Republican nominee for the White House.
Criticising the billionaire’s anti-immigrant rhetoric, the Pope said: “Anyone, whoever he is, who only wants to build walls and not bridges is not a Christian.”
Mr Trump retorted: “For a religious leader to question a person’s faith is disgraceful.”
Meanwhile, the president has signed an executive order designed to ease a ban on political activity by churches.
The order also includes regulatory relief to religious employers that object to contraception.
It does not permit denying services to gay people in the name of religious freedom, as was feared by rights groups.
The American Civil Liberties Union said it would file a lawsuit challenging the order.