The couple, who welcomed their first child together on 24 June 2016, also revealed they named her ‘Milena’, shortened to ‘Mila’.
Rihanoff, 38, had a “difficult” 19-hour labour, where the cord was wrapped around Milena’s neck.
“I can’t even begin to describe the pain, but it’s an incredibly proud moment when you see your baby for the first time,” she told Hello!
“It’s an incredible feeling of love.”
Cohen, 37, who already has twin eight-year-old daughters Isabelle and Harriette with former wife Abby Cohen, said he was “very proud” of Rihanoff.
“Kristina was amazing,” he added. “Milena has changed the dynamic - another little human in our lives. She is our creation and that is amazing.”
The couple met as dancing partners on Strictly Come Dancing 2013. Cohen and his former wife announced their separation in September 2014.
Cohen and Rihanoff have always insisted they only got together after Cohen split from Abby.
At the time of announcing her pregnancy, Rihanoff told HELLO! it was a “surprise”, but she was “obviously delighted”.
Read the full interview with Kristina Rihanoff and Ben Cohen in the new issue of Hello! out now.