The Finance and Public Administration committee will run the ruler over changes made to the Commonwealth bureaucracy since the Coalition won power in 2013, after a Labor motion passed the Senate on Tuesday.

It will hope to answer the question of whether the APS transformation and modernisation projects initiated since the 2014 budget achieved what they were supposed to.

It will also examine the public service's digital capability and workforce, which The Canberra Times has confirmed will include the average staffing level cap and the use of contractors and consultants.

Labor's public service spokeswoman, Senator Katy Gallagher, said the pandemic had demonstrated just how important the work of the public service was to Australians.

"The APS has designed, implemented and managed the Australian response to COVID-19, including in providing financial support payments to millions of Australians, in protecting our borders and by working to secure a vaccine against the coronavirus," Senator Gallagher said.

However Labor helped to jettison a proposal from the Greens for a Senate inquiry into decades of privatisation and corporatisation within government.

Greens leader Adam Bandt accused Labor of a "political stitch-up".

"In an act of parliamentary cowardice, Labor joined the Liberals to create a weaker inquiry that they would control from go to whoa," Mr Bandt said.

"The terms of reference in this political stitch-up fail to investigate the corporatisation of the public service, the sale of government assets, or the results of the sale of Qantas, Commonwealth Bank, and the corporatisation of Australia Post."

During Estimates, it was revealed the cost of public-sector contracting had blown out to $4.8 billion in the last five years.

The size of the permanent public service workforce fell from 152,000 in June 2013 to 132,000 in June 2019.