The deal was sealed with Hess' $US17.5 million ($A16.24 million) payment to Falcon's Australian subsidiary, Falcon Australia.
Hess Oil and Gas Holdings also paid Falcon $2.
HESS Australia and Falcon Oil and Gas have finalised a Beetaloo Basin participation and evaluation deal which may see Hess take a 62.5% stake in the exploration permits 76, 98 and 117.
The deal was sealed with Hess' $US17.5 million ($A16.24 million) payment to Falcon's Australian subsidiary, Falcon Australia.
Hess Oil and Gas Holdings also paid Falcon $2.