Deputy leader Larissa Waters moved to establish the inquiry which ended up passing the Senate on Wednesday after One Nation's Pauline Hanson gave it her support.
The federal government has earmarked the Beetaloo as a key basin it is seeking to develop as part of its gas-led recovery.
The inquiry will probe not only whether the spending is worth taxpayers' money, but the social and environmental consequences of oil and gas exploration and production in the region.
"The wins keep coming," Greens Leader Adam Bandt tweeted.
"The Senate just voted to establish a Greens-chaired inquiry into oil & gas exploration in the Beetaloo Basin. You can always trust us to fight this fossil-fuelled government."
The inquiry's establishment was cheered by activist groups including GetUp! and 350 Australia.
"This is a huge win for Traditional Owners and Territorians who are calling to protect country and stop public money flowing to fossil fuel companies," GetUp tweeted.
The government has committed hundreds of millions of dollars to developing the Beetaloo, including granting A$50 million in exploration grants, along with the A$250 million Beetaloo Strategic Basin Plan released in January.
Funding will fast track drilling by providing to cover 25% of eligible exploration costs, capped at A$7.5 million per well and three wells per exploration venture.
The development has the support of the Northern Territory government and the federal Labor opposition, with shadow resources minister Madeline King telling APPEA last week that it would provide crucial jobs and investment in the region.
The Greens have argued for months that First Nations communities and farmers remain strongly opposed to fraccing due to perceived risks of groundwater contamination. The powerful Northern Territory Cattlemen's Association has long had issues with gas development, also.
The party has also highlighted the CSIRO's discovery earlier in the year of complex ecosystems in several interconnected aquifers across the basin.