At least seven others – including police personnel – were injured in the attacks, authorities said.
The first two went off within minutes of each other, with the third two hours later. The explosions happened near a police post outside the university’s faculty of engineering.
State television named the officer as Tariq al-Mirjawi, the head of Giza governorate’s investigation department.
The bombings were the latest in a campaign of attacks targeting Egypt’s police and military that began with the ousting last summer of Islamist president Mohammed Morsi.
The attacks are taking place amid a crackdown by security forces against pro-Morsi protesters and members of Mr Morsi’s Muslim Brotherhood.
The staggered nature of the blasts in a relatively close area was new, analysts said last night.
The first two bombs – which security officials said were hidden at the foot of a tree – went off less than a minute apart. A third was concealed up another tree.
The first two blasts killed two and wounded seven, officials said. No-one was harmed by the last explosion. State TV described the bombs as “crude and homemade”.
Cairo University, along with other campuses, has been a major centre for the near daily protests by pro-Morsi students against the military-backed interim government since the months-long crackdown has largely crushed protests elsewhere. The university protests often turn into clashes with security forces.
Yesterday’s bombs appeared to target riot police deployed outside the university to confront any protests, though none was going on at the time of the blasts.
One media agency reported that four civilians and three senior police officers, including Major General Abdel-Raouf El-Sirafy – who is the deputy chief of police in the Giza province, parts of which are located in the Greater Cairo area – were among those injured.
Egypt has suffered a series of suicide bombings, car bombings and assassination targeting security forces. An al-Qaeda-inspired militant group based in the Sinai Peninsula called Ansar Beit al-Maqdis has taken responsibility for most of them.
Cruder bombings have also targeted police patrols and positions in the street, often claimed by lesser-known groups.
The military-backed interim government has branded Mr Morsi’s Muslim Brotherhood a terrorist group, accusing it of organising the campaign of violence while it pushes ahead with protests against Mr Morsi’s removal by the military.
Hundreds of Islamists have been killed and more than 16,000 arrested in authorities’ bid to crush the Brotherhood. The group denies any link to terror organisations.
It says the prosecution of its members is intended to give a legal veneer to what it sees as the illegal removal of an elected president.