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. (+ video) » | Wednesday, August 14, 2013
BBC: Sky News cameraman Mick Deane shot and killed in Egypt : A veteran Sky News cameraman has been shot and killed while covering the violence in Cairo, the broadcaster has said. » | Wednesday, August 14, 2013
