Bashir's decision to dismiss the entire government was approved by the top leaders of his ruling National Congress Party (NCP) at a late-night meeting.
The decision to form a new government comes as Sudan faces a growing economic crisis triggered by an acute shortage of foreign exchange and rising inflation of more than 65 percent.
"The economic situation must be resolved and for this President Bashir decided to cut the government at all levels," said Faisal Hassan Ibrahim, one of Bashir's main advisers, after the PNC meeting.
"President Bashir has decided to have a smaller government of 21 members," he said. The outgoing cabinet was made up of 31 ministers led by Prime Minister Bakri Hassan Saleh, who was also the first vice president.
Bashir appointed Moutaz Mousa Abdallah, who was minister of irrigation in the outgoing cabinet, as the new prime minister, while Saleh will remain the first vice president.
Bashir also appointed Mohamed Osman Yousif Kiber as vice president.
Ibrahim said that Abdallah had been entrusted with the task of forming the new cabinet, but it was not clear when he would take the oath.
Earlier on Sunday, the presidency announced Bashir's decision to dismiss the Saleh government "to fix the situation facing the country."
"He (Bashir) will form a new government that can once again bring hope to the Sudanese people," the presidency said.
Deepening the crisis
Sudan's economic conditions have only worsened, as the cost of food products and other products has more than doubled in the last year, while the currency market has seen the Sudanese pound sink against the US dollar.
The central bank has devalued twice the pound this year, and is currently trading at 41 per dollar on the black market. The official rate is 28 per dollar.
The economic crisis in Sudan was first highlighted in April, when then Foreign Minister Ibrahim Ghandour announced in parliament that he had not been able to pay the salaries of his staff for months due to a shortage of funds. He was immediately fired.
Days after Bashir fired Ghandour, he announced a major reorganization of the cabinet that replaced the ministers of oil, interior, agriculture, youth and sports and justice. The reorganization also aimed to face the economic crisis.
The economic crisis in Sudan has deepened despite the fact that the United States lifted its decades-old trade embargo imposed on the African country in October.
Expectations that the lifting of sanctions would help revive Sudan's troubled economy have so far not materialized.
Although Washington lifted the embargo, it still holds Sudan on its list of "state sponsors of terrorism," a factor officials say keeps investors away from Sudan.
Sudan's economy is already suffering the loss of three quarters of its oil resources when South Sudan gained independence in 2011.
The World Bank and other global financial institutions have urged Sudan to adopt rapid structural reforms to revive its economy in crisis.
The average growth of Sudan's gross domestic product between 1998 and 2008 was more than six percent, after which it steadily declined.
Previous efforts in economic reform have proved controversial.
An attempt in September 2013 to cut fuel subsidies led to bloody clashes between protesters against austerity and security forces that left dozens dead in Khartoum.
In January, Sudan again witnessed sporadic anti-government protests after a sharp rise in food prices.
Authorities quickly mobilized to stop these protests by arresting several activists and opposition leaders.
In August, the PNC chose Bashir as a candidate for the 2020 presidential election.