The family first appeared on Gogglebox in their first episode in 2013, but announced in 2014 that they were leaving because Michael was fighting for Ukip in the national election.
After failing to secure a seat for Hastings and Rye, the family returned with future episodes of the show.
The statement, issued by PA Media, said: "We are deeply saddened by the passing of Gogglebox star Andy Michael at the age of 61 following a short illness. Andy died last weekend with his family next to him.
“Andy, a retired businessman who brought a lot of wisdom and insight to Gogglebox, was one of the first actors in the show, appearing in the first episode in 2013.
“Katy's beloved father, Alex, Pascal and Louis, and Carolyne's husband, Andy, were a much-loved and respected member of the Gogglebox family, and they will be missed.
“Our love and thoughts are with Carolyne and the whole family. The family has asked to be alone at this very sad time ”.
Earlier this week, it was announced that fellow Gogglebox star Mary Cook passed away at the age of 92.