The duo, who have grown close since spending time together in the Big Brother house, will be filmed as their very different lives collide.
Bercow, the wife of the Speaker of the House of Commons, will move in with Big Fat Gypsy Weddings star Doherty for two weeks and experience the life of a traveller.
The political activist will take on domestic duties and live among Doherty's large family of children and grandchildren.
In the second week of the challenge, Bercow will be able to set rules and challenges for Doherty including a cleaning rota and the task of cooking a meal for his family.
"When Paddy Met Sally explores the unlikeliest of celebrity friendships in a unique and entertaining setting," said Initial creative director Nick Samwell-Smith.
"When two very different worlds collide, viewers can expect conflict, debate and a whole lot of fun. Whatever happens, after two weeks living in each other's pockets, their lives will never be quite the same again."
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Watch Paddy Doherty discuss his Celebrity Big Brother win below: