Kevin announced he was walking away from the BBC dance show after seven years in a post on his Instagram Story and Twitter account on Friday.
Kevin - who won the 2018 series with partner Stacey - said he wanted to “leave on a high” in an emotional message to fans.
Following his announcement, The Sun ran a story claiming Stacey encouraged the professional dancer to “go it alone” so they could become a “TV power couple”.
On Saturday, Stacey described the claims as “utter nonsense”, labelling the The Sun’s story “embarrassing”.
“Honestly, we knew this would happen. And so it starts, again...... Utter nonsense,” she tweeted.
She then added: “‘TV power couple’. Give. Me. A. Break. These articles are so, so embarrassing.”
Kevin joined the show in 2013 with then-girlfriend Karen Hauer. The pair married in 2015, before announcing their split in 2018.
During his time on the show, Kevin was paired with Susanna Reid, Frankie Bridge, Kellie Bright, Louise Redknapp, Susan Calman, Stacey Dooley and Anneka Rice.
He reached five Strictly finals before lifting the Glitterball trophy for the first time in 2018 with Stacey, who he is now in a relationship with.
The BBC said Kevin would be “hugely missed” by his fans and colleagues.
Paying tribute, a spokesperson for the show said: “Kevin has been such a brilliant part of Strictly for the past seven years.
“From reaching the final an impressive five times, to lifting the Glitterball with Stacey Dooley in 2018, he has provided the show with some fantastic moments, through his exceptional talent as a dancer and choreographer. He will be hugely missed by fans and by his Strictly family.
“He will always be our Kevin from Grimsby.”
Strictly Come Dancing returns to BBC One in the autumn.