The musician died in his sleep in the early hours of Saturday after suffering organ failure.
A statement shared their Twitter page read: "It is with tremendous sadness that we announce the passing of our very own Chas Hodges.
"Despite receiving successful treatment for oesophageal cancer recently, Chas suffered organ failure and passed away peacefully in his sleep in the early hours of this morning."
Chas, whose full name was Charles, "passed away peacefully" in his sleep in the early hours of Saturday, according to a statement on their website.
The statement continued: "We would like to thank our fans for their fantastic support and goodwill at this difficult time."
The homepage of their website was replaced with a photo tribute to Chas.
Chas & Dave were a popular English pop duo and were known for performing 'rockney', a mix of singalong, humour, and rock.
They had a string of hits, including Rabbit, Snooker Loopy and Ain't No Pleasing You.
As the news of Chas's death broke, musicians, comedians and fans paid tribute to the star.
Comedian Sir Lenny Henry tweeted: "What a shame. When they were on Tiswas they were always kind, respectful and played live. RIP Chas."
Comedy writer and author Adam Kay tweeted: "Sad news. The very least we could do in Chas' memory is make "Ain't No Pleasing You" the new national anthem. Belting tune."
Comedian Rob Beckett joined in with those paying tribute to Hodges.
He tweeted: "So sad. Such a legend. Together with Dave he wrote the soundtrack to my childhood. RIP Chas Hodges."
Radio DJ and TV presenter Iain Lee tweeted: "Absolutely gutted about @ChasnHodges passing.
"Was always a real gentleman to me and very generous with his time. Absolutely one of the best. Played piano at Eric Clapton's wedding. The other members of the spontaneous band? Paul McCartney, Ringo Starr and George Harrison."
The official Twitter account for Tottenham Hotspur Football Club - of which Hodges was an outspoken supporter - posted: "Everyone at the Club is deeply saddened to hear of the passing of one of our own, Chas Hodges.
"Our thoughts are with his family and friends at this difficult time."
In August, the duo had been forced to cancel their forthcoming shows following doctor's advice regarding Chas's health.
Earlier this summer, Chas and Dave supported Eric Clapton at the British Summer Time festival in Hyde Park.