Rinehart also has a 10 per cent stake in Channel Ten, Australia's third-largest television network, and a seat on the board.
Rinehart's wealth is based on the vast Pilbara mine holdings she inherited from her father Lang Hancock.
This month, she sold 15 per cent of Hancock Prospecting's stake in the Pilbara Roy Hill project to South Korea's Posco, reportedly doubling her wealth to almost A$20 billion.
Rinehart topped last year's BRW Rich List, and Citigroup estimated that she could overtake American Wal-Mart heiress Christy Walton as the world's richest woman and, possibly, eclipse Mexico's Carlos Slim and Microsoft's Bill Gates to become the wealthiest person on the planet.
Concerns over her Fairfax move have centred on the potential influence she could exert on governments. She is a powerful advocate of mining interests and has campaigned against Labor's mining and carbon taxes.
Communications Minister Stephen Conroy said Rinehart's Fairfax play emphasised the need for a public interest test on media diversity.
But Senator Conroy joined Finance Minister Penny Wong, Shadow Treasurer Joe Hockey, and the journalists' union and media analysts in saying that Rinehart was unlikely to be able to force her views on Fairfax editors.
"All that's really changing is that a different wealthy individual is taking a strategic or ownership position in some media," he said.