The appointment of Sheikh Nawaf al-Ahmed al-Sabah was announced on Tuesday, as was the appointment of Sheikh Nasser Mohammed al-Ahmed al-Sabah as Kuwait's new prime minister.
Sheikh Nawaf is the amir's half-brother and has held the post of first deputy prime minister since 2003, while Sheikh Nasser has been the minister of the amiri court since 1998.
To become effective the crown prince's appointment needs to be approved by a majority in the oil-rich emirate's elected parliament.
Under the constitution, the new premier, a nephew of the amir, has two weeks to form a government which must first be approved by the amir and take the oath of office in parliament before assuming power.
The two men are from the Al-Jaber branch of the Al-Sabah ruling family, which by tradition has been alternating the leadership of the state with the Al-Salem branch for the past 85 years.
The appointment follows a crisis of succession in Kuwait that saw Sheikh Saad al-Abdallah al-Sabah, the former ailing amir voted out of office after only nine days in power following the death of his predecessor Sheikh Jaber al-Ahmad al-Sabah on 15 January.
Sheikh Nawaf, the new crown
prince, is the amir's half brother
Sheikh Sabah was later nominated as new ruler and was confirmed by parliament on 29 January. He was sworn in the same day.
Under the constitution, the amir has the sole authority to appoint his crown prince and prime minister.
Sheikh Nawaf, 68, became a minister for the first time in 1978.
He was later appointed to several other posts including that of defence, until after the liberation of Kuwait from Iraqi occupation in 1991.
In 2001, he was appointed deputy head of the national guard, until 2003, when he was re-appointed to the cabinet.