Bashir scrapped the post after leading a bloodless coup against then-premier Sadiq al-Mahdi with the help of Hassan al-Turabi.
Sudanese lawmakers voted Wednesday to bring back the post of prime minister, a position abolished after President Omar al-Bashir came to power in a 1989 Islamist-backed coup.
The move to delegate limited powers to a prime minister fits with reforms proposed by a national dialogue between Bashir's government and some opposition groups.
Bashir scrapped the post after leading a bloodless coup against then-premier Sadiq al-Mahdi with the help of Mahdi's brother-in-law, Islamist leader Hassan al-Turabi.
In October, after a quarter-century in power, Bashir concluded a year-long national dialogue aimed at resolving the 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.
On October 10, Bashir submitted a "national document" to serve as a framework for a new Sudanese constitution.
That led to Wednesday's amendment, approved by all 387 MPs present out of a total of 425.
While it gives the prime minister responsibility for "executive power in the country", it still allows the president to form a government or sack ministers.
Sudan currently has a transitional constitution adopted in 2005, ahead of the country's north-south split in 2011 following two decades of civil war.