Officials had earlier said Rouhalamini and Kamrani died of meningitis.
"The coroner rejected that these people died of meningitis and confirmed there were bruises on their bodies from beatings and that the cause of death was a series of beatings," the prosecution office's said.
Neither the names of the three defendants nor the posts they held at Kahrizak were cited in the report.
However, the statement said that another nine members of staff will also face prosecution in the Kahrizak case and that all have now been indicted, adding that trial dates and charges would be announced in due course.
|Protests after presidential elections were the biggest in the Islamic Republic's history [AFP]
The detention centre, which was ordered closed in late July by Ayatollah Ali Khamenei, Iran's supreme leader "had unsuitable hygienic, nutrition and living conditions without medical care".
"Because of space limitations ... many of the arrested people ... were held together with some thugs.
"Abnormal and physical punishments by the guards also aggravated this bad situation," the government statement read.
The prosecution statement explained that the Kahrizak lawsuit was based on 98 complaints, of which 51 were withdrawn on the basis of compensation.
It also said that 168 protesters were taken to the detention centre between June 25 and July 10.
Iranian officials have put the number of people killed during the protests at 36, but opposition groups say at least 72 people have died in post-election incidents.
More than 4,000 arrests were made in Tehran and Iran's major cities. Most have since been released but some 140, among them well-known figures, have been put on trial and some of them have received heavy sentences.
Hundreds of thousands of protesters gathered in Tehran following the Islamic republic's June 12 presidential election to protest against the result, alleging the poll was rigged.
In an unprecedented crackdown on opposition supporters, scores of senior reformist politicians and journalists were rounded up, in addition to thousands of protesters.