The pair were forced to leave the BBC ballroom competition last week after Katya tested positive for Covid-19.
They will now return to the show in the coming weeks for a non-competitive routine.
Nicola revealed the news during an appearance on spin-off show It Takes Two on Wednesday, saying: “Well as my saying goes I do like doing the most. Me and Katya will be coming back.”
Prior to the series, Strictly bosses had warned stars that they would be axed from the show if either person in their pairings tested positive for the virus.
Strictly rules have always allowed injured or sick stars a one-week bye in previous years, but the two-week isolation period means that contestants forced to quarantine would be out of the competition for too long.
The Olympic boxer, who is currently self isolating, admitted it had been strange watching the show from home.
Appearing via video link, she said: “It was a bit weird not being part of the show but I have to say everybody did amazingly. There were 10s being thrown out and Anton did great as well.”
Nicola, who had made Strictly history with Katya as part of the show’s first-ever same-sex couple, also spoke of her frustration at having to exit the competition after scoring well with the judges.
She said: “It was a little bit frustrating not being able to continue when I had just got back into the swing of things and I was enjoying the dance and everything.
“But the rules are in place to keep everybody safe so I’m doing my part.”
A Strictly spokesperson previously insisted the couple would not be allowed to return to the show in a competitive capacity.
“They’re not allowed to re-enter the competition after they’ve taken part in the first episode,” they said in a statement read out on ITV’s Loose Women.
“Nicola can’t come back because she will have an unfair advantage in the future as she’s now had weeks of training,”
Strictly Come Dancing continues on Saturday at 7.15pm on BBC One, while It Takes Two airs weeknights at 6.30pm on BBC Two.