The 53-year old joined BHP's board in September 2016, and competed with fellow directors Lindsay Maxsted and Malcolm Broomhead for the role.
Elliott in response said it supported the appointment as a first step in bringing much-needed change to the direction of the company.
BHP made the announcement on Friday morning after a meeting of the BHP board in Chile this week. Mackenzie is expected to tackle calls to dump its oil business and overhaul the board.
The New York-based fund's call for new directors and a review of management has shifted some of the focus to the future of CEO Andrew Mackenzie, in his position since 2013 and who met with Elliott for talks in May.
Shaw and Partners mining analyst Peter O'Connor said MacKenzie would face a chorus of shareholders seeking change and rejuvenation of the board.
In late 2015, a burst dam at Samarco, a joint venture between BHP and Brazil's Vale, killed 19 people and caused the country's worst environmental disaster as mud and waste destroyed a village and polluted the Rio Doce river.
Before that, Tribeca said it had been holding private talks with a number of possible candidates for BHP's board and has pushed for BHP to sell its US oil-and-gas assets.
MacKenzie will succeed Jacques Nasser, 69, a former Ford Motor Co.
"With the assistance of Heidrick & Struggles, a leading worldwide recruitment firm, the Board undertook a rigorous search and assessment of potential external and internal candidates against clear skills and performance criteria".
Senior independent director Shriti Vadera said Mr MacKenzie had a proven track record of delivering value for shareholders and extensive global executive experience.
Despite being the world's biggest mining house, BHP has a history of appointing executives from outside the sector as chairs.
MacKenzie grew up in Canada and started his career at Accenture.
Oversupply in some markets, coupled with industrial reforms, a transitioning economy and slower growth in China, the top commodities consumer, pose risks to materials prices, according to the World Bank.