The 135-kilometer (84-mile) railway, which will link mining operations to a river terminal, will cost an estimated $1.2 billion and is expected to start operations in 2022.
Most workers at Gold Fields' struggling South Deep mine have been on strike since Nov. 2 over the company's plans to cut around 1,100 jobs, or 30% of its workforce.
La Mancha is a private gold company with investments in Toronto-listed Endeavour Mining, Australia's Evolution Mining and Ghana-focused Golden Star Resources.