Prince Salman bin Abdulaziz, who is 76, will take the defence post, state television al-Ekhbariya announced.
He is currently governor of Riyadh and is the half-brother of King Abdullah.
Interior Minister Prince Nayef bin Abdulaziz had already been named as crown prince and Prince Sutam bin Abdul Aziz will become Riyadh's new governor.
Saudi Arabia is one of the world's biggest arms spenders, and Prince Salman is expected to continue building strong ties with Western allies.
One former diplomat has described him as "intelligent, political, in touch with the conservative base, but also quite modern-minded," Reuters news agency reported.
Another ex-diplomat said Prince Salman had always been "very helpful" in resolving difficulties facing Westerners in the kingdom.
Saudi Arabia has named a new defence minister after the death of Crown Prince Sultan, who had held the defence position for some 50 years.