Bakri Hassan Saleh was named prime minister by the executive bureau of Bashir's National Congress Party (NCP).
"He will take the oath as prime minister tomorrow," Ibrahim Mahmoud, the NCP's deputy chief, told reporters yesterday, adding that Saleh would also hold onto his current post of Sudan's first vice president.
Sudanese lawmakers voted in December to reinstate the post of prime minister.
Following the appointment of Saleh, a fellow officer involved in the Islamist-backed coup, Bashir is expected to announce a cabinet reshuffle on Thursday.
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In October, after a quarter century in power, Bashir concluded the national dialogue aimed at resolving insurgencies in Sudan's border regions and healing the country's crisis-wracked economy.
The talks launched in October 2015 were boycotted by most mainstream opposition and armed groups.
Bashir abolished the post of premier after he led a bloodless coup almost three decades ago against then premier Sadiq al-Mahdi with the help of Islamist leader Hassan al-Turabi.
A fixture of Sudanese politics since the 1960s, Mahdi served as prime minister from 1966 to 1967 and again from 1986 to 1989.
His government was the last to be democratically elected in Sudan before the 1989 coup.