GRAM agreed to up its offer from $1.71 per share to $1.85 per share after PanAust slammed the initial bid as opportunistic.
Independent expert EY previously assessed the fair value of PanAust shares to be $1.84-2.04 per share.
PanAust chairman Garry Hounsell said the unanimous recommendation was made following careful consideration.
"GRAM's revised offer enables our shareholders to realise a compelling premium for their shares and provides certain cash value," he said.
"The PanAust Laos business continues to perform strongly and the Frieda River project is a substantial long term growth asset for the company.
"The board has considered the long-term value potential of these assets and the risks associated with delivering this value and on balance has formed the view that the revised GRAM offer represents the best option for PanAust shareholders to realise a premium value at this time for their shares."
The offer price represents a 51% premium to PanAust's closing price before the initial offer was announced in late March.
GRAM has a 24.2% stake in PanAust already, making a third party bid unlikely.
"GRAM has been a supportive shareholder since 2009 and it is encouraging that through the offer they have endorsed the company's strategy as well as the management and employees who ultimately are responsible for making PanAust the high quality company that it is today," Hounsell said.
"GRAM is well-placed to support the long-term strategy of the company, including the development of the Frieda River Project in PNG."
The offer will close on May 15.
PanAust has commenced trading after calling a trading halt on Friday, with shares listed at $1.85 per share this morning.