They were expected to oversee the signing of agreements between American and Saudi companies, including one between Saudi oil giant Aramco and several US companies.
The two leaders signed a joint vision agreement Saturday at the Saudi Royal Court and sealed it with a handshake.
The arms sale agreement was just one of a series of deals to be announced during the visit, with USA conglomerate General Electric saying it had also signed agreements and memorandums of understanding worth $15 billion.
The two countries also announced a defense cooperation agreement and private sector agreements Saturday that are meant to create tens of thousands of new jobs in the USA defense industry.
White House officials hope the trip gives Trump the opportunity to recalibrate after one of the most hard stretches of his young presidency.
The arms announcement comes amid new private sector agreements after U.S. and Saudi Arabian companies gathered Tuesday for a Saudi-U.S. CEO Forum here.
The White House says the agreements include military sales of about $100 billion, effective immediately, plus another $350 billion over the next 10 years.
It will also bolster the kingdom's "ability to contribute to counter-terrorism operations across the region, reducing the burden on the United States military to conduct those operations", the official added.
Trump and Salman were expected to oversee the signing on Saturday afternoon of multiple agreements between American and Saudi companies, including between the Saudi oil giant Aramco and various U.S. firms. The two leaders shared a long drive from the airport to central Riyadh, where the President is staying, and Trump was due to spent much of Saturday in meetings with Salman and his government, including the powerful deputy crown prince Mohammed bin Salman. White House aides view the address as a counter to Obama's 2009 speech to the Muslim world, which Trump criticized as too apologetic for US actions in the region.
On visits earlier this year, British Prime Minister Theresa May and German Chancellor Angela Merkel also shunned head coverings.
President Donald Trump and first lady Melania Trump step off Air Force One upon arrival at King Khalid International Airport in Riyadh on Saturday. As he arrived, Trump told the king the spectacle was "very impressive".
"They did not use the global multi-lateral platform such as Organisation of Islamic Cooperation (OIC) as they just wanted to invite all OIC members minus the two - Iran and Syria - for the summit", said the diplomat.
Trump's daughter, Ivanka, a senior White House adviser who is also accompanying her father, also left her head uncovered.
Mr Trump made no substantial remarks on his first day overseas and spent most of his time shuttling between opulent palace ballrooms with the king.
"Riyadh's visit, an opportunity for Trump to fix his image with the Muslim world", said a diplomat from an Asean member country. During the Obamas' visit, Mr Trump tweeted, "Many people are saying it was wonderful that Mrs Obama refusing to wear a scarf in Saudi Arabia, but they were insulted". The grand welcome - which featured a military brass band and a fighter jet flyover - demonstrated just how highly anticipated Trump's arrival was to this Middle Eastern kingdom.
The trip, which includes stops in Israel, Rome, Brussels and Sicily, is likely to shine an unaccustomed spotlight on the president's wife, who hasn't moved into the White House or staffed an office there.
Mrs. Trump wore a black pantsuit with a golden belt and did not cover her head, consistent with the custom for foreign dignitaries visiting Saudi Arabia.
Trump tweeted several photographs from the welcoming ceremony.
President Donald Trump is preparing for a busy day of meetings in Saudi Arabia.
White House aides had hoped Trump's ambitious foreign swing would provide relief from a barrage of bad headlines.
He broke with tradition by not going to neighbouring countries such as Canada and Mexico first before heading for other countries like most of the past presidents did.
The president began his visit with a coffee ceremony with King Salman of Saudi Arabia.
Trump dodged one potential land mine when Sudanese President Omar al-Bashir, who has been indicted on war crime and genocide charges, announced that he would not attend the summit for personal reasons. For one, they've praised Trump's rhetoric about Iran posing a threat to the nation.
Trump's luxury hotel was bathed in red, white and blue lights and, at times, an image of the president's face.