Atlanta-born Jordan, whose civil rights career evolved to high-profile Washington lawyer, has passed away aged 85.
Brian Mulroney, chairman of the board and former Canadian prime minister, said Barrick was deeply saddened by Jordan's death.
"He was a vigorous and effective participant in all advisory board debates that concerned the company, its future, its employees and the social and political environments in which Barrick operates around the world," Mulroney said.
"We shall miss his brilliance, great good humour and sound judgement he brought to bear on all subjects under board consideration and we shall remember him with affection and respect as a valuable colleague and a loyal friend."
Chair of law firm Akin Gump, Kim Koopersmith, said colleague and mentor Jordan was one of a kind and would be greatly missed.
"To the world, Mr Jordan was a towering civil rights figure, a confidant to presidents and a counsellor to CEOs and governments around the globe," she said.
"And he was all of those things. But to us at Akin Gump, he was also a wise and trusted mentor and friend who, in all that he did, inspired us to be the best possible version of ourselves.
"Mr Jordan's generosity was boundless, and his guidance was unassailable and delivered with a purposefulness and moral clarity that will never be equalled."
Barrick's international advisory board members include Spain's former prime minister Jose Maria Aznar, former US speaker of the house of representatives Newt Gingrich and former German defence minister Karl-Theodor zu Guttenberg.