Rumours that the actors were dating began circulating on Saturday and speaking outside his London home, Hugh addressed the claims.
He told the Mail On Sunday: “I am very, very happy, we are so very happy… It’s nice and yes, it’s so lovely.”
The paper adds that the couple have been together since last year, living in a penthouse flat Hugh purchased after his 2015 split from second wife, Kate Abbot-Anderson.
The comedian has two children, aged 21 and 19, from his marriage to Kate.
Claire split from her husband, Charles Palmer, two-and-a-half years ago but kept the split under wraps by reportedly continuing to refer to him as “my husband”.
Claire and Charles also have two children together, aged 19 and 16. It’s believed their families already knew about the relationship.
In their initial report, the Sun quoted a source as saying that “there has been some talk within the acting world of them being an item” for weeks.
They added: “It’s the most wonderful love story, they found one another at the right time in their lives and it’s all rather sweet.”
Hugh and Claire played ‘Outnumbered’ parents Pete and Sue Brockman for seven years, with the final episode of the fifth series airing in 2014.
A Christmas special followed in 2016, pulling in over 7 million viewers.