Thornton will remain as executive chairman, directing strategy and Bristow will be president and chief executive of the merged company, running day-to-day operations.
The new company will keep the Barrick name and be listed in NY and Toronto, while Randgold's London listing will be cancelled.
The two companies said they were aligned on their strategy with Chinese investors after Barrick said it would make a bigger push to attract investors in China.
Bristow acknowledged that the industry has always been criticised for its "short-term focus, undisciplined growth and poor returns".
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. Randgold's London listing will be cancelled. Randgold shareholders will hold the rest. Shares of Barrick, the world's second largest gold producer, were up 6.3 percent in afternoon trade in Toronto.
Barrick and Randgold are hoping that joining forces and combining their huge resources will help them weather the storm.
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"The 59-year-old has arguably reached the pinnacle of his career with this deal, yet he will be under considerable pressure to make sure shareholders are not left with an inferior company to a standalone Randgold".
The deal value, at 48.5 pound-a-share, matched Randgold's market capitalization as of Friday's close.
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.
Each Randgold Shareholder will receive: 6.1280 new Barrick shares for each Randgold share. Randgold has also slipped this year as it faced labor challenges in the Ivory Coast, a tax dispute in Mali and the prospect of a tougher mining code in the Democratic Republic of Congo.
Bristow added on another call that the new company would be open to weighing options for its Nevada and Australia assets, and said there had expressions of interest on the latter.
Nicholas Hyett, equity analyst at Hargreaves Lansdown, said: "From Randgold's perspective the deal diversifies exposure away from high-risk African markets and towards Barrick's more stable North American assets".