Bashir's order came three days after a prominent insurgent group freed dozens of prisoners, mostly soldiers, it had captured in fighting with government forces.
"The decision to pardon 259 rebels aims at preparing the environment for achieving lasting peace in the country," Bashir's office said in a statement.
Those pardoned include 66 rebels who had been sentenced to death.
Of the 259 rebels to be released now, dozens were captured in 2015 after fierce fighting in war-torn South Darfur between government forces and rebels.
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Forty-four rebels also among those pardoned were captured in the city of Omdurman in 2008 after similar clashes between government forces and JEM fighters.
"The decision to pardon is a progressive step and would help in the ceasing of hostilities," Nur Ahmed al-Nur, editor-in-chief of Assayha newspaper, told AFP.
On Sunday, another prominent rebel group, the Sudan People's Liberation Movement-North (SPLM-N), freed at least 125 prisoners, mostly soldiers.
The prisoners had been captured in Blue Nile and South Kordofan states, where the SPLM-N has been fighting government forces for years.
At least 300,000 people have been killed in Darfur and another 2.5 million displaced since the conflict erupted, the United Nations says.
In 2011, similar rebellions against Bashir's regime also broke out in Blue Nile and South Kordofan states.
Khartoum announced a unilateral ceasefire in June 2016 in all three conflict zones, which it extended by six months in January.
Bashir, who has ruled Sudan for nearly three decades, is wanted by the International Criminal Court for alleged war crimes in Darfur. He steadfastly denies the charge.