Ibrahim, 62, replaces General Jamal al-Din Omar who died of an unspecified illness while in neighbouring South Sudan for peace talks with the country's main rebel groups.
His appointment came a year after long-time autocrat Omar Bashir was toppled in mass protests in April 2019.
"We will work side by side doing our best... to achieve the goals of the constitutional declaration," the official SUNA news agency quoted Ibrahim as saying after he was sworn in.
Since August last year a transitional government, comprised of civilians and military officials, has taken over the reins of power in Sudan after political factions adopted a constitutional declaration.
The declaration paved the way for the new government to steer the country to civilian rule during a three-year transition.
But the transition has been fragile with the government facing major challenges, including soaring inflation, a huge public debt, tribal clashes and efforts to forge peace with rebels.
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