The couple, who married in 2015, said they are still partners on a professional level and will continue with their joint tour, which kicks off in May.
Kevin told BBC Radio 2’s Chris Evans: “We wanted to let everyone know that privately we’re not together anymore, but professionally we are stronger than ever.
“Dance has always been the thing… dance is how we came together and has been the glue that held us together for years now.
“We’re still the best of friends, we’ve got a lot of love and respect for each other, I still pretty much see Karen every day.”
Karen joked that he will “never get rid of me”.
They said they wanted to speak out and “be upfront” with their fans because there had been “a lot of talk” about their relationship in recent months.
Kevin said: “What we’ve found is, since we’ve been honest with each other about our relationship, it’s unlocked a new wealth of creativity.
“We feel like we’re stronger than ever and taking our dance partnership and professional relationship to the next level now, which is why we’re so excited about this tour.”
Karen said: “We have such great chemistry and for us it’s all about the storytelling and giving the best performance.”
The dancers were hit with reports that their marriage was in trouble during the most recent series of Strictly.
It had been claimed that the pair had fallen victim to the “Strictly curse” and had been “barely speaking” after Kevin began training with comedian Susan Calman in Scotland.