The prosecutor's decision follows the cancer deaths of people who worked at the company's Ivrea factory in north-west Italy between the 1970s and 1990s, La Stampa reported.
A complaint was first filed six years ago by the family of a woman who died from malignant mesothelioma, a form of cancer linked to asbestos exposure. The woman worked at the factory from 1965 to 1980 and died in 2007.
The other workers all became ill after 2003 with the same form of cancer, the newspaper said.
Carrado Passera, Olivetti's CEO between 1992 and 1996 is among the 20 people under investigation for manslaughter along with Carlo De Benedetti, the company's president between 1978 and 1996.
Olivetti and those who led the company during that period are accused of failing to take sufficient measures to protect the workers from asbestos exposure.