In October 2016 the Mother and Baby Homes Commission of Investigation began test excavations at the site in Tuam.
The commission was established following allegations about the deaths of 800 babies in Tuam and the manner in which they were buried.
It said it was "shocked" by the discovery.
The Tuam home was one of 10 institutions in which about 35,000 unmarried pregnant women are thought to have been sent.
A child died nearly every two weeks between the mid-1920s and 1960s.
In a statement on Friday, the Mother and Baby Homes Commission of Investigation said the remains were found in "at least 17 of the 20 underground chambers which were examined earlier this year".
It added: "These remains involved a number of individuals with age-at-death ranges from approximately 35 foetal weeks to two-three years."
The home operated from 1925 to 1961 and a number of the samples are likely to date from the 1950s, the commission said.
The commission said it is continuing its investigation into who was responsible for the disposal of human remains in this way and has asked that the relevant state authorities take responsibility for the appropriate treatment of the remains.
The coroner has been informed.
"Significant quantities" of human remains have been discovered at the site of a former mother and baby home in County Galway.