The deal will see South Africa's state-owned oil company, Strategic Fuel Fund (SFF), and South Sudan's Nile Petroleum Corporation, explore an area of 31,000 square kilometres (12,000 square miles) known as "Block B2".
Exploration will begin immediately, and is expected to continue for six years.
The country has the third-largest oil reserves in sub-Saharan Africa, according to the ministry.
A September 2018 peace deal has helped revive production, which has gone from around 155,000 barrels per day (bpd) at the end of last year, to current figures of 175,000, said Gatkuoth.
He said the government was aiming to reach 200,000 bpd by the end of 2019.
The oil sector's revival was a key part of the peace deal mediated by Sudan, whose economy also suffered from the slowdown in oil output to the south.
The agreement with South Africa is part of a deal signed in November 2018 that will see Pretoria invest around $1 billion (880 million euros) in the oil industry, money that would go towards building a refinery and pipelines as well as oil exploration and training of workers and engineers.
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