"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."
Austrian 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.
"A legend has left us. Rest in peace Niki #nikilauda," tweeted 2009 world champion and former McLaren driver Jenson Button as social media exploded with the news of his death.
Former motorcycling world champion Casey Stoner said on Twitter: "RIP Niki Lauda, a true Icon and Motorsport legend. Thoughts are with his family and loved ones at this time."
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 had severe burns to 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.
He missed only two races that season but was unable to hold off the challenge of Britain's James Hunt, who went on to claim his only world title.
The rivalry between the two men -- which demonstrated the Austrian's extraordinary courage and fighting spirit -- was portrayed in the 2013 film "Rush" by American director Ron Howard.
The next season, in 1977, Lauda went on to win his second Formula One world championship with Ferrari.
He quit Formula One at the end of 1979 to pursue his second passion, civil aviation.
But he came back to the race circuit in 1982, this time with McLaren, and won his last world championship with them in 1984.
Lauda underwent an emergency lung transplant in a Vienna hospital in August 2 last year after contracting an infection in his lungs, which were scarred and weakened by the effects of inhaling high temperature smoke during the 1976 accident.
Years before he had also received kidney transplants. When one failed, a second kidney was donated by his then-girlfriend Birgit Wetzinger, a former flight attendant, who he married in 2008.
Besides their twins, a boy and a girl born in 2009, Lauda also had three other sons from previous relationships.