The pair made the announcement today (August 18) on social media ahead of the new series of Strictly.
The split comes a year on from the Katya and Seann Walsh kissing scandal that made front page news during 2018's series.
In a post shared on both their Instagram pages, Katya and Neil wrote: "Hi everyone, 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."
They continued: "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 projects."
The message added: "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 xx."
Earlier this year Neil and Katya had played down last year's kiss drama, after photos emerged of Katya kissing her celebrity partner Seann.
At the time, both issued grovelling apologies and made a sombre appearance on spin-off show It Takes Two.
In an interview with the Daily Mail, Neil recalled: "It was a shock. And we had to work it out between ourselves, to understand what had happened.
"But I wasn’t going to allow that one little thing to get in the way of ten very happy years."
He added: "I’m private. I’m also quite positive. I wanted to speak to Katya – we had to sort it out privately."
"Every love story has its ups and downs," Katya added. "No relationship is perfect. I think people can relate to that."
"I apologised when it happened, and I’m happy to apologise again now," she told the publication. "I made a mistake, but I don’t want that one mistake to jeopardise everything we’ve built.
"And it hasn’t. We have our trust back."
Strictly Come Dancing 2019 will launch next month on BBC One with both Neil and Katya confirmed to return as pro dancers.
Alongside Neil, the male pros are AJ Pritchard Aljaž Škorjanec, Anton Du Beke, Giovanni Pernice, Gorka Marquez, Graziano Di Prima, Johannes Radebe and Kevin Clifton. Pasha Kovalev won't be returning having decided to quit after 8 years.
The women joining the pro cast together with Katya are Amy Dowden, Dianne Buswell, Janette Manrara, Karen Clifton,, Luba Mushtuk, Nadiya Bychkova, Oti Mabuse and new pro dancer Nancy Xu.