Gold Fields has offered 35 of its own shares for every 100 shares in Western Areas which owns half of South Deep, one of the world's deepest gold mines.
The offer is one part of three related deals worth $2.5 billion by Gold Fields to gain control of South Deep.
At the beginning of the month, the miner completed the purchase of Barrick Gold's 50 percent stake in South Deep and rival Harmony Gold said it would tender its 29.2 percent stake in Western Areas.
Buying the stake held by Canada's Barrick cost $1.52 billion, consisting of $1.2 billion in cash and 18.7 million of its own shares.
Last month, Gold Fields said it had concluded the first transaction, to buy a 34.7 percent stake in Western Areas owned by JCI Ltd.