The professional dancer and the former rugby player met on the BBC show in 2013 and Cohen, 44, has proposed during a holiday in the Maldives.
Rihanoff, 45, told Hello magazine: "It was absolutely surreal and I couldn't believe what was happening. I'm usually very perceptive... How he managed to keep it a secret was amazing...
"Although we'd talked before about getting married one day, I hadn't the slightest idea that Ben was planning this. I was overcome with emotion and said: 'Yes, yes and yes' straight away."
Cohen said: "I wanted us to go further forward together and taking a holiday in such a beautiful place felt like the perfect moment to do that."
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The couple were struck by the Strictly curse during the 11th series of the dance contest, when they fell for one another, despite Cohen having been married for 11 years to Abby Blayney, with whom he shares twin daughters.
Cohen said: "Love has different meanings and for me, that's a relationship with a partner who's been through difficult times with me and together we move forward. She's the person I want in my life forever."
Rihanoff and Cohen welcomed their own daughter, Milena, in 2016.
The Russian dancer was previously hit by the Strictly curse in 2009, when she was partnered with boxer Joe Calzaghe. He split with his girlfriend of five years, Jo-Emma Larvin after falling for Rihanoff. They split in 2013.
Cohen and Blayney divorced in 2016.
Photographer Blayney said in 2021: "At the time of the break-up, when hugely stressed, I once angrily referred to Ben's partner as a 'f**king Russian dancer' to a journalist hassling me. I regret that now.
"I'm happier in my own skin and I'm not that broken girl who used to be married to a famous rugby player."
Rihanoff retired from the show in 2015 and took part in Celebrity Big Brother in 2016.