Hip-hop mogul Russell Simmons's website GlobalGrind.com first reported the death of the hip-hop icon, which came at the end of a long battle with cancer.
Yauch, also known by his stage name MCA, was diagnosed with the disease back in July 2009, originally resulting in the cancellation of the group's tour and the delay of their album Hot Sauce Committee.
Bandmate Adam 'Ad-Rock' Horovitz confirmed that the star was still receiving treatment last May.
Yauch's publicist has now said: "It is with great sadness that we confirm that musician, rapper, activist and director Adam 'MCA' Yauch... passed away in his native New York City this morning after a near-three-year battle with cancer."
> Adam Yauch 1964-2012 - Obituary
> Adam Yauch 1964-2012 - Life in pictures
The musician founded the New York group in 1979 with Mike D, Mix Master Mike and Ad-Rock.
Under the alias Nathanial Hörnblowér, Yauch directed many of the Beastie Boys' most memorable music videos.
Beastie Boys won three Grammy Awards, two in 1999 and another in 2008.
Yauch is survived by his wife Dechen and daughter Tenzin Losel.
> Adam Yauch 1964-2012 - Reactions
> Adam Yauch 1964-2012 - Beastie Boys' five classic music videos
Photo gallery: Adam Yauch's life and career in pictures:
Copyright: Rex Features Everett Collection
Watch the video for classic Beastie Boys track 'Intergalactic' below: