The company's shares will be traded on Riyadh’s Tadawul stock exchange.
The president tweeted that he's authorized the release of strategic petroleum reserves "if needed" to stabilize energy markets after an attack on Saudi oil sites.
Yemen's Houthi rebels have claimed responsibility for the attacks in Buqyaq and the Khurais oil field.
One of them was reportedly en route to pick up Saudi oil to take to the United States.
The changes appear to further consolidate the crown prince’s grip on power by appointing advisers and members of the royal family seen as close to him.
"Some of those they are harshly treating have been 'milking' their country for years!" the president said on Twitter.
A $110 billion deal in which Saudi Arabia will buy U.S. arms, with options running as high as $350 billion over 10 years, was the central achievement of Trump’s first day in Riyadh.
To encourage such stability and protect busy trade routes, Japan seeks to assert a more active role in the region as a promoter of conflict resolution.