"With deep sadness, we announce that our beloved Niki has peacefully passed away with his family on Monday," the statement read.
Lauda's death comes eight months after he underwent a lung transplant.
"His unique achievements as an athlete and entrepreneur are and will remain unforgettable, his tireless zest for action, his straightforwardness and his courage remain," added the statement.
"A role model and a benchmark for all of us, he was a loving and caring husband, father and grandfather away from the public, and he will be missed."
Lauda won the Formula One drivers' world championship three times, in 1975 and 1977 for Ferrari and in 1984 with McLaren.
"All at McLaren are deeply saddened to learn that our friend, colleague and 1984 Formula 1 World Champion, Niki Lauda, has passed away. Niki will forever be in our hearts and enshrined in our history. #RIPNiki," his former team tweeted on their verified account.
Lauda had been non-executive chairman at Mercedes F1 since 2012 and he was instrumental in bringing in Lewis Hamilton to spark a run of success that has brought five consecutive world drivers' and constructors' championships.
During his driving career, Lauda suffered horrific injuries on August 1, 1976 when, having already won five races that season, his vehicle burst into flames on the Nuerburgring in Germany.
He suffered severe burns on his face and hands, and inhaled toxic fumes which damaged his lungs.
Despite being given the last rites in hospital he made an almost miraculous recovery to race again just six weeks later still bandaged and in intense pain.