They celebrated their sixth wedding anniversary earlier this month, and have been together for 11 years.
Neil and Katya have not blamed Seann Walsh for their split, but indicated their marriage had become more a friendship than a romance.
The Strictly Come Dancing professionals were the focus of national headlines following a scandal on the dance show in 2018 involving comedian Walsh.
Russian choreographer Katya was pictured sharing a kiss with her then dance partner on a night out during the last series of Strictly.
The incident led to the pair performing a "dance of shame" on the show, as the media scrutinised another instance of the so-called Strictly curse.
Neil and Katya remained together following the scandal, and have said the well-publicised incident was not the cause of their split.
In an official statement released today, the couple said their relationship had mellowed into a friendship.
The dancers themselves have thanked fans for their supports, and expressed how proud they are of their shared achievements.
In a joint statement they said: "As our fans and loyal supporters you are really important to us and so we wanted to let you know some news.
"After 11 years, we have made the mutual decision to separate.
"We will always love each other, just in a different way as friends. This will never change what a great team we make and we are really proud of everything we have achieved together.
"Our shared love of dance means we will keep working and dancing together as well as exploring individual projects. No matter what we do we will always support and respect each other.
"We wish one another every happiness and we will remain the best of friends. We are really looking forward to getting back to the ballroom and can't wait to keep on dancing.
"Lots of love from us both."
A spokeswoman for the pair clarified that their decision to part was not influenced by the controversy surrounding Walsh which made front-page news.
Stating that the decision was made recently, a spokeswoman said: "It would be incorrect and unfair to attribute their separation to one isolated incident.
"Many people make such a decision to separate when they realise that their relationship has become more of a friendship.
"They remain the very best of friends and will continue to dance together."
The dancers added that their professional lives and their careers on Strictly would not be impacted by the split.
She said: "They're incredible close, they are still dance partners, will be dancing together and will work on joint projects together as well as being part of the Strictly team and will continue to give each other advice and support in any individual projects."
Speaking in March 2019, the couple told Lorraine Kelly that they had moved on from the incident.
Neil said regarding the public and media attention surrounding the kiss: "For me, I felt they overreacted."
Katya said: "We're over it, I think everyone else is over it, let's just move on."
In August 2019, the pair posted on their social media accounts celebrating six years of marriage.
Neil said he was still "jumping with joy".