The family first appeared on Gogglebox in the debut episode in 2013, but announced in 2014 that they were leaving because Mr Michael was running for Ukip in the general election.
After he failed to secure the Hastings and Rye seat, the family returned for future episodes.
The statement, given to the PA news agency, said: "We are deeply saddened to share the passing of Gogglebox star Andy Michael at the age of 61 following a short illness.
"Andy passed away last weekend with his family by his side.
"Retired hotelier Andy, who brought much wit and insight to Gogglebox, was one of the show's original cast members, appearing in the very first episode in 2013.
"Beloved father to Katy, Alex, Pascal and Louis, and cherished husband of Carolyne, Andy was a much-loved and respected member of the Gogglebox family, and he will be very sadly missed.
"Our love and thoughts are with Carolyne and the entire family. The family have asked for privacy at this very sad time".
Earlier this week it was announced that Gogglebox star Mary Cook had died at the age of 92.
