
The camps had been occupied by supporters of former president Mohammed Morsi, who was deposed in early July.
Security forces say 95 people have been killed, but the Muslim Brotherhood says hundreds have died.
The state of emergency will begin at 16:00 local time (1400 GMT), and last for a month.
Shortly after dawn on Wednesday morning, armoured bulldozers moved deep into the main protest camp outside the eastern Rabaa al-Adawiya mosque.
Officials say the other protest camp, at Nahda Square, has now been cleared.
Graphic accounts of bloodshed emerged from the protest camps as reporters described wounded protesters being treated next to the dead in makeshift field hospitals.
The 17-year-old daughter of leading Muslim Brotherhood figure Mohamed el-Beltagy was among the dead, reports say. Asmaa el-Beltagy was shot in the back and chest, her brother said.
A cameraman working for Sky News, Mick Deane has also been killed in the violence.
There were reports of unrest elsewhere in Egypt. At least five people have been killed in the province of Suez, according to the health ministry. Witnesses say Morsi supporters attempted to storm government buildings there.
It is still unclear how many casualties were caught up in the two Cairo operations. Figures differ widely and have been impossible to verify independently.
The health ministry has issued an official death toll of 95. The interior ministry denied any deaths were caused by its forces firing live ammunition.
The government has meanwhile congratulated the security forces on their operation to clear the camps.
In a televised statement, a government spokesman praised their “self-restraint” and spoke of the “smaller number” of injuries among protesters.
The government would decisively confront attempts to attack state buildings and police stations, he said.
Source: bbc.com/news
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