The change came among a series of orders issued by the king, who shuffled his cabinet, restored civil service benefits, and replaced the head of the army which for two years has been fighting rebels in neighbouring Yemen.
"Prince Abdullah bin Faisal bin Turki removed as ambassador to the US. Prince Khaled bin Salman bin Abdulaziz appointed ambassador," the official Saudi Press Agency reported, citing a royal order.
Prince Abdullah had served for just over a year, according to the website of the Saudi embassy in Washington.
The United States and Saudi Arabia have a decades-old relationship based on the exchange of American security for Saudi oil.
But ties between Riyadh and Washington became increasingly frayed during the administration of president Barack Obama.
Saudi leaders felt Obama was reluctant to get involved in the civil war in Syria and was tilting toward Riyadh's regional rival Iran.
The Saudis have found a more favourable ear in Washington under Trump, who took office in January and has denounced Iran's "harmful influence" in the Middle East.
Washington provides some logistical and intelligence support, as well as weapons, for the Saudi-led coalition in Yemen.
The kingdom also belongs to the US-led coalition against the Islamic State group in Iraq and Syria.
Prince Khaled, the new ambassador, is an air force pilot who flew missions as part of that anti-IS coalition, said Salman al-Ansari, president of the Saudi American Public Relation Affairs Committee (SAPRAC).
Ansari, whose committee is a private initiative to strengthen Saudi-US ties, described Prince Khaled as a "very organised personality, savvy, youthful, and active."
Another son of King Salman, Deputy Crown Prince Mohammed bin Salman, 31, is second in line to the throne and is one of the kingdom's most powerful figures.
He holds the post of defence minister and is pushing a wide-ranging social and economic reform programme.
- Military bonuses -
Among other orders issued by King Salman, the head of the army Lieutenant General Eid al-Shalwi was removed. Fahad Bin Turki was promoted to replace him.
The army is helping to defend Saudi Arabia's southern border from rebel incursions but analysts say that, in Yemen itself, coalition troops from the United Arab Emirates have the most prominence in ground operations being conducted with local forces.
Saudi Arabia leads the air campaign but after two years of coalition intervention analysts say Yemen is more unstable than ever, and one called it a "quagmire".
Saudi military personnel in the Yemen operation will receive a salary bonus of two months, the king also ordered, despite a budget deficit forecast to be $53 billion this year following a collapse in global oil prices since 2014.
The salaries of other civil servants were frozen last year and benefits curbed, while the government cut subsidies and delayed major projects.
Salman on Saturday ended the restrictions on compensation for state workers because he is "keen to provide comfort to the Saudi citizens," a decree said, as the kingdom prepares to increase electricity and other prices.
Salman fired Minister of Civil Service Khaled al-Araj, who will be investigated by a committee of the Royal Court.
The Arab News reported late last year that Araj was under investigation by the kingdom's anti-corruption commission for the alleged "irregular hiring" of his son.
In other changes, Salman dismissed Minister of Information and Culture Adel al-Turaifi and replaced him with Awad al-Awad.
Minister of Communication and Information Technology Mohammed al-Suwaiyel also lost his job, replaced by Abdullah al-Swaha.
The king changed some regional governors, along with numerous senior bureaucrats including the head of the General Authority of Sports as the kingdom tries to provide more athletic activities for its people.
Under the reforms being directed by the Deputy Crown Prince, Saudi Arabia is trying to make government operations more efficient and officials more accountable.