Barrick executive chairman John Thornton will hold the same role at New Barrick while Randgold chief executive Mark Bristow, who co-founded the company in 1995, will become CEO of the combined company.
Each Randgold investor would receive, the pair said, 6.1280 new Barrick shares for every Randgold share.
Barrick's majority-owned Acacia Mining Plc has been stuck in limbo after Tanzania imposed a ban on exports of mineral concentrates in 2017 and slapped a US$190 billion tax bill on the London-listed company.
Two of the world's largest gold miners have announced plans to merge in a deal that will create a global leader with a market value of £14bn.
Bristow acknowledged that the industry has always been criticised for its "short-term focus, undisciplined growth and poor returns".
As part of the deal, China's Shandong Gold, one of the country's biggest gold producers, has agreed to buy $300 million of shares in Barrick.
"By employing a strategy similar to the one that proved very successful at Randgold, but on a larger scale, the new Barrick Group will leverage some of the world's best mines and talent to create real value for all stakeholders".
The companies are reported to have been talking about a possible tie-up for three years...
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"Mr Bristow has struck gold, in a sense, as he now becomes the boss of the world's biggest gold miner", said AJ Bell investment director Russ Mould.
Exchange ratio has been agreed based on the volume-weighted average prices of Barrick shares traded on NYSE, and Randgold ADSs traded on Nasdaq over the 20 trading days ended on September 21.
The creation of a gold mining company with a combined market value of about $18 billion helps Barrick to boost output at a time when its stock has been punished for the producer's stagnant pipeline, according to Bloomberg.
In 2017, Barrick and Randgold combined produced 6.64 million ounces while the next largest gold miner, Newmont, churned out 5.27 million ounces.
Following completion of the Merger, Barrick shareholders will own approximately 66.6% and Randgold shareholders will own approximately 33.4%.
The merger between Barrick and Randgold remains subject to shareholder approval.
"From Randgold's perspective the deal diversifies exposure away from high-risk African markets and towards Barrick's more stable North American assets".