The agreements included an $110bn arms deal, which the White House described as the single biggest in US history.
Mr Trump and his wife Melania were greeted in the Saudi capital by King Salman on Saturday morning local time.
The eight-day trip comes as Mr Trump faces uproar at home following his sacking of FBI director James Comey.
It will also take in Israel, the Palestinian territories, Brussels, the Vatican, and Sicily.
US Secretary of State Rex Tillerson said the arms deal was aimed at countering the “malign” influence of Iran.
“The package of defence equipment and services supports the long-term security of Saudi Arabia and the entire Gulf region,” he told a news conference in Riyadh.
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 administration.
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 criticised then-First Lady Michelle Obama for doing the same. In a tweet, Mr Trump said she had “insulted” her hosts.
On Sunday, Mr Trump will attend the Arab Islamic American Summit in Riyadh and speak about his “hopes of a peaceful vision of Islam”. Aides say the president hopes his speech will resonate worldwide and express “a common vision of peace, progress and prosperity”.
Mr Trump caused controversy during his campaign by calling for Muslims to be temporarily banned from entering the US over security concerns. Legislation aimed at restricting travel from several Muslim-majority countries remains tied up in the US courts.
The summit agenda is expected to focus on combating Islamist militants and the growing regional influence of Iran.
Mr Trump has been a fierce critic of the international deal with Iran which eased sanctions in return for a curb on its nuclear activities.
Unlike his predecessor, Barack Obama, he is not expected to highlight human rights during his trip.
In a tweet, King Salman praised Mr Trump, adding that he hoped his visit would “strengthen our strategic co-operation”. He later handed the US President Saudi Arabia’s highest civilian honour, the King Abdulaziz medal.