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.

Commissioners at the agency voted two-to-one to end a "net neutrality" order enacted in 2015.
Ajit Pai, head of the FCC, said the rules demanding an open internet harmed jobs and discouraged investment.
Many Americans and technology firms filed objections to the FCC's proposal prior to the vote.
"This is the right way to go," said Mr Pai ahead of the vote on Thursday.
In a statement, the FCC said it expected its proposed changes to "substantially benefit consumers and the marketplace". It added that, before the rules were changed in 2015, they helped to preserve a "flourishing free and open internet for almost 20 years".
The vote by the FCC commissioners is the first stage in the process of dismantling the net neutrality regulations.
The agency is now inviting public comment on whether it should indeed dismantle the rules. Americans have until mid-August to share their views with the FCC.
This call for comments is likely to attract a huge number of responses. Prior to the vote, more than 1 million statements supporting net neutrality were filed on the FCC site.
Many people responded to a call from comedian and commentator John Oliver to make their feelings known.
Separately, some protestors also used software bots to repeatedly file statements on the site.
Many fear that once the equal access rules go, ISPs will start blocking and throttling some data while letting other packets travel on "fast lanes" because firms have paid more to reach customers quicker.
US ISPs such as Comcast, Charter Communications and Altice NV have pledged in public statements to keep data flowing freely.
Despite this public pledge Comcast, along with Verizon and AT&T, opposed the original 2015 rule change saying it dented their enthusiasm for improving US broadband.
Facebook, and Google's parent company Alphabet as well as many other net firms have backed the open net rules saying equal access was important for all.
"Significant quantities" of human remains have been discovered at the site of a former mother and baby home in County Galway.
[NEXT_CONCEPT]
The US Federal Communications Commission has voted to overturn rules that force ISPs to treat all data traffic as equal.