It will be led by Mullah Mohammad Hassan Akhund, one of the movement's founders, who is on a UN blacklist.
The interior minister will be a feared FBI-wanted leader of the Haqqani militant group.
The Taliban seized control of most of the country on 15 August, ousting the previous elected leadership.
The announcement of the acting cabinet is a key step in the formation of a Taliban government.
A statement attributed to Taliban Supreme Leader Mawlawi Hibatullah Akhundzada told the government to uphold Sharia law.
The Taliban want "strong and healthy relations with our neighbours and all other countries based on mutual respect and interaction", the statement, released in English, said - with the caveat that they would respect international laws and treaties "that are not in conflict with Islamic law and the country's national values".
Hibatullah Akhundzada has never made a public appearance. This is the first message appearing to come from him since the Taliban took control last month.
The Taliban have previously said they wanted to form an inclusive government. However, all of the cabinet ministers announced on Tuesday are already established Taliban leaders.
Hassan Akhund, the new prime minister, served as deputy foreign minister from 1996 to 2001, when the group were last in power.
Sirajuddin Haqqani, the new acting interior minister, is head of the militant group known as the Haqqani network who are affiliated with the Taliban and have been behind some of the deadliest attacks in the country's two-decade-long war - including a truck bomb explosion in Kabul in 2017 that killed more than 150 people.
Unlike the wider Taliban, the Haqqani network has been designated a foreign terrorist organisation by the US. It also maintains close ties to al-Qaeda.
According to the FBI's profile on Haqqani, he is "wanted for questioning in connection with the January 2008 attack on a hotel in Kabul... that killed six people, including an American citizen".
It adds: "He is believed to have coordinated and participated in cross-border attacks against United States and coalition forces in Afghanistan. Haqqani also allegedly was involved in the planning of the assassination attempt on [former] Afghan President Hamid Karzai in 2008."
The Haqqani network has also been blamed for an attack on the US embassy and nearby Nato bases in Kabul on 12 September 2011. Eight people - four police officers and four civilians - were killed in that attack.
