Prince Mohammed warmly greeted Trump on Tuesday as he stepped off Air Force One and kicked off his Middle East tour.
The two leaders then retreated to a grand hall at the Riyadh airport for a coffee ceremony.
The crown prince will fete Trump with a formal dinner and, later on Tuesday, the president is slated to take part later in a US-Saudi investment conference.
On Wednesday, Trump will join a gathering of members of the Gulf Co-operation Council - made up of Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates - before leaving Riyadh.
Saudi Arabia and fellow OPEC+ nations have already helped their cause with Trump early in his second term by stepping up oil production.
Trump sees cheap energy as a key component to lowering costs and stemming inflation for Americans.
The president has also made the case that lower oil prices will hasten an end to Russia's war on Ukraine.
But Saudi Arabia's economy remains heavily dependent on oil, and the kingdom needs a break-even oil price of $USS96 dollars to $US98 a barrel to balance its budget.
It's questionable how long OPEC+ is willing to keep production elevated. The price of a barrel of Brent crude closed Monday at $US64.77.
Trump picked the kingdom for his first stop because it has pledged to make big investments in the US, but Trump ended up travelling to Italy in April for Pope Francis's funeral.
Riyadh was the first overseas stop of his first term.
The three countries on the president's itinerary - Saudi Arabia, Qatar and the United Arab Emirates - are all places where the Trump Organization, run by Trump's two elder sons, is developing major real estate projects.
They include a high-rise tower in Jeddah, a luxury hotel in Dubai and a golf course and villa complex in Qatar.
Trump is trying to demonstrate that his transactional strategy for international politics is paying dividends as he faces criticism from Democrats who say his global tariff war and approach to Russia's war on Ukraine are isolating the United States from allies.
He is expected to announce deals with the three wealthy countries that will touch on artificial intelligence, expanding energy co-operation and perhaps new arms sales to Saudi Arabia.
The administration earlier this month announced initial approval to sell $US3.5 billion ($A5.5 billion) worth of air-to-air missiles for Saudi Arabia's fighter jets.
Trump has also said he might travel on Thursday to Turkey for potential face-to-face talks between Russian President Vladimir Putin and Ukrainian President Volodymyr Zelenskiy on Russia's war in Ukraine.
Meanwhile, Trump has said he will decide during the trip how the US government will refer to the body of water now commonly known as the Persian Gulf.
He told reporters that he expects his hosts will ask him about the US officially calling the waterway the Arabian Gulf or Gulf of Arabia.
Abbas Aragachi, the Iranian foreign minister, has warned that changing how the US refers to the waterway would compel the "wrath of all Iranians from all walks of life and political persuasion in Iran, the US and across the world".
with Reuters
