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The US$380 million deal was announced in December, with Teranga saying it had now also been granted formal approval to integrate the operations.
In a presentation, Teranga said it would prioritise mining Massawa's higher-grade ore and was targeting first gold production in the second half of 2020.
"The combination of the two assets results in significant capital and operating synergies and creates a top-tier gold complex," president and CEO Richard Young said.
The company paid upfront about $300 million in cash and issued $80 million in shares to Barrick and Compagnie Sénégalaise de Transports Transatlantiques Afrique de l'Ouest SA, which together owned 90% of Massawa.
A later payment of up to $50 million is due in three years with its value contingent on the average gold price for the period.
"Barrick will participate in the upside of the combined asset through the 11% interest it is acquiring in Teranga through this transaction," Barrick president and CEO Mark Bristow said.
He described Massawa as "one of the largest unexploited gold deposits in West Africa" which legacy company Randgold Resources had progressed.
The project was deemed non-core after Randgold's merger with Barrick.
Massawa has historical mineral reserves of 2.6 million ounces of gold at 3.94g/t and a feasibility study by Barrick in 2019 put the after-tax NPV5 at $677 million and the IRR at 41%, using a $1,400/oz gold price.
The Senegal government has a 10% interest in both Massawa and Sabodala.
Teranga also recently declared commercial production at its Wahgnion gold mine in Burkina Faso and has other exploration projects in West Africa.
Its shares have undergone a re-rating, nearly tripling from May 2019's low of C$2.98 to a peak of $8.86 in February.
They closed down 0.95% yesterday to $7.28 to capitalise it about $784 million (US$585 million).