The remains were found covered by sheets in various parts of the house in Evanston on Friday but no foul play was suspected.
Authorities said one of the siblings was last seen alive in the 1980s, the second in 2003 and the third in May.
The woman living in the house, described as "upwards of 90 years of age," was cooperating in the investigation and was taken to a facility for care.
Authorities, who did not release the names of the deceased, said a care worker had alerted them to the situation. Autopsies were due to be performed on Saturday.