The TV presenter, who has been guest hosting This Morning over the summer, is married to Daly who has fronted the BBC One contest since it began in 2004.
He told The Sun how the show had been with them through key moments in their lives, including the arrival of their daughters Phoebe and Amber, now 17 and 13.
Kay said: “We love Strictly in our house. It’s like our third child. Tess started the show in its infancy — its first ever series when it was just a wee baby.
“Then we had our first baby and subsequently we had Amber, so we’ve grown up with it as like a family member."
He continued that it "sleeps for most of the year", but "comes alive" in August when show preparations begin.
Asked whether Daly, 53, would still be on the show into her 80s like her former co-host Sir Bruce Forsyth, who died in 2017 aged 89 and made his last Strictly appearance in 2015, he said: "Yes, I think so".
Kay, 48, also praised her partnership with Claudia Winkleman as hosts of the show after the late Sir Bruce retired.
He spoke about how proud they both were to be the first female double act to present a prime time entertainment show, saying they had "broken the mould".
Kay added: “I think that’s something that both of them are really proud of — and long may it continue.”
Strictly is due to return to BBC One on 17 September and has announced its celebrity cast, which includes Matt Goss, Helen Skelton and Fleur East.
Daly and Winkleman are back to host, and the same judging panel as last series will return - Shirley Ballas, Craig Revel Horwood, Motsi Mabuse and Anton Du Beke.
Watch: Who is Strictly's Matt Goss?