Mudawi Ibrahim Adam, an engineering professor at the University of Khartoum, was arrested by security forces in December as part of a crackdown against opposition leaders and activists.
Under Sudanese law, the charges against him were punishable by death.
Prosecutors had accused Ibrahim Adam of being among activists who were running a criminal organisation and engaged in spying and intelligence activities for foreign embassies.
Ibrahim Adam and others were also accused of "publishing lies about (government forces) using chemical weapons" during fighting with rebels in the country's conflict zones.
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"I am issuing a decision to pardon... Dr Mudawi Ibrahim Adam," Bashir said in a decree signed today and quoted by the official SUNA news agency.
Bashir also pardoned five other activists, the agency said.
It was not immediately clear when he would be released from jail.
Several opposition leaders and activists were detained in December in a bid to crush widespread protests against a government decision to raise fuel prices.
Ibrahim Adam, who has worked extensively on human rights issues in Sudan, has been arrested several times for his work. The government shut down a development organisation he headed in 2009.
Ibrahim Adam's "arbitrary arrest underscores the government's desperate attempts to extinguish the last embers of dissent in the country", Amnesty International said soon after he was detained.