Earlier on Wednesday, Labor leader Anthony Albanese said the committee was needed to examine how the government was responding to the coronavirus pandemic.
"That will ensure there is oversight during this period. That is very important indeed," he said.
The seven-member Select Committee on COVID-19 will be chaired by Labor's finance spokesperson Katy Gallagher.
Liberal Senator James Paterson will be the government's nominee as the committee's deputy chair.
"Parliamentary scrutiny remains important in times of crisis," Senator Paterson said in a statement.
"Given the extraordinary measures governments have been required to implement to tackle COVID-19, it is more important than ever."
Overall, the committee includes three Labor senators, two coalition senators, one Greens senator, and independent Jacqui Lambie.
The committee will have broad terms of reference to look at all aspects of the government's response to the pandemic.
Labor's preference was for a scaled-down parliament to meet regularly during the pandemic, but the government moved to suspend sittings.
The government has said parliament can be recalled if needed, but politicians should follow health advice to stay home.
Lower House crossbench MPs Andrew Wilkie, Helen Haines, Rebekha Sharkie, Adam Bandt and Zali Steggall have called for separate coronavirus economic and health committees.
Ms Steggall said oversight was important.
"There needs to be flexibility to ensure decisions have the intended effect and oversight to ensure there is no abuse of the system," she said.
The Australia Institute think tank has released a poll showing two-thirds of people support having a parliamentary committee looking into Australia's coronavirus response.
About one in eight people opposed the idea, the poll showed.
People in Australia must stay at least 1.5 metres away from others and gatherings are limited to two people unless you are with your family or household.
If you believe you may have contracted the virus, call your doctor (don’t visit) or contact the national Coronavirus Health Information Hotline on 1800 020 080. If you are struggling to breathe or experiencing a medical emergency, call 000.
SBS is committed to informing Australia’s diverse communities about the latest COVID-19 developments. News and information is available in 63 languages at sbs.com.au/coronavirus.
With additional reporting from AAP