Swearing allegiance to a new king is a requirement imposed by the country's constitution.
Saudi Arabia's royal court swore allegiance to King Salman soon after the announcement of the death of his predecessor, King Abdullah bin Abdulaziz, earlier on Friday.
The court said King Salman had issued orders that citizens swear allegiance to his crown prince, Muqrin bin Abdulaziz.
"Citizens are expected to swear allegiance to the new king, crown prince and deputy crown prince later on Friday," the court said in a statement.
King Salman has appointed Mohamed bin Naif, 56, as deputy crown prince. Bin Naif will also maintain his post as interior minister.
Bin Naif is the first grandchild of late Saudi King Abdulaziz Al Saud to be appointed deputy crown prince.
King Abdullah was declared dead on Friday at 91 years old after having been admitted to hospital three weeks earlier.