Assad tasked Khamis with forming a new government, the official news agency SANA reported.
He is to submit his proposal for new ministerial appointments in the coming days.
The 54-year-old engineer replaces Wael al-Halqi who had held the post since August 2012.
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The changes come two months after Assad's Baath party and its allies won a majority of seats in parliamentary elections dismissed internationally as a sham.
Khamis had served as Syria's minister of electricity since 2011 and is an electrical engineer by trade.
Since March 2012, he has been sanctioned by the European Union, which accuses him of sharing "responsibility for the regime's violent repression against the civilian population."
Syria's conflict began in 2011 with widespread protests demanding reform but has since escalated into a bloody civil war that has left 280,000 people dead.
According to the government, production of electricity has more than halved since the beginning of the crisis.