The Cairo court building was encircled by dozens of black-clad security forces.
Mustafa and al-Sukkari, who were placed in the caged-off area for suspects with a partition between them, did not react to the judge's pronouncement.
Their lawyers said they will appeal within 60 days.
Mustafa was a member of the Shura Council, the upper house of Egypt's parliament, representing the ruling National Democratic Party, and was widely reputed to have been a close associate of Hosni Mubarak, the president, and his son.
The case has drawn a media frenzy in Egypt and throughout the Middle East.
Tamim rose to stardom in the late 1990s but then hit troubled times, separating from her Lebanese husband-manager, who filed a series of lawsuits against her.
During interrogations, Mustafa said he broke up with Tamim, describing her as a former lover, after his mother opposed the couple's marriage plan.
Motives behind the killing are not yet known.
According to Dubai investigators, al-Sukkari stalked Tamim to her apartment in the Dubai Marina complex and entered using an ID of the management company from which she had recently bought her place.
Blood-soaked clothes were found dumped outside the building, and police say the killer's face was captured on security camera footage.