On completion of the agreement, Origin and Sasol will each hold 35% in each of the permits, with Falcon owning the remaining 30%.
All up, the permits, about 500km southeast of Darwin, cover more than 18,500sq.km.
Origin will pay Falcon $11 million on completion of the deal and will take on the role of operator, contributing an additional $32 million during the three years of the exploration stage.
Origin and Sasol will each have the option to pursue another two stages in 2017 and 2018, costing Origin an estimated $25 million and $24 million respectively.
"This farm-in provides Origin a significant unconventional exploration position in one of the Northern Territory's most prospective onshore basins," Origin upstream CEO Paul Zealand said.
"Previous exploration activities within the Beetaloo Basin, including drilling activity on the permits, have highlighted its strong shale gas potential.
"The signing of this farm-in agreement is consistent with our objective to find new sources of energy.
"Upon success, these resources could then be monetised by connecting them with domestic and international markets."
The deal is still conditional on various approvals, with Origin willing to acquire Sasol's interest if the company does not obtain regulatory approval for its stake.