The court also sentenced three other police officers to suspended sentences of one year each on the same charges.
The deputy sheriff, Amr Farouk, and the three other officers, Ibrahim Mohamed El-Morsi, Islam Abdel-Fattah Helmi, and Mohamed Yahia Abdel-Aziz, all worked at Masr El-Gedida police station in north-eastern Cairo.
On 18 August, 37 people -- described by the interior ministry as being supporters of ousted president Mohamed Morsi who had been arrested at protests -- died of asphyxiation due to teargas and overcrowding while they were being transferred to Abu Zabaal prison in Cairo in a police van.
Prosecution investigated the case, questioning seven survivors of the incident and another 40 people including police, forensic doctors and a representative from the justice ministry, Al-Ahram Arabic news website reported.
Investigations showed that the police van transferring the prisoners only had the capacity to hold 24 people. At the time of the incident, 45 people were inside.
Security forces claimed the prisoners had died during an escape attempt. However, the prosecution later said this was inaccurate.
Prosecution said the policemen dealt with the prisoners with negligence, recklessness and lack of precautions, breaching their duties to maintain citizens’ safety, regardless of whether they were suspected of crimes.
Egyptian police have long been accused of using excessive force and torture . The January 2011 revolution which led to the ouster of Hosni Mubarak  was partially spurred by anger at police brutality.
In December the Egyptian government declared the Muslim Brotherhood a terrorist organisation , accusing it of complicity in ongoing militant attacks on Egyptian security forces which have claimed dozens of lives. A crackdown on the group has seen thousands of members jailed on a variety of charges.