The musician and presenter said her family feel “blessed and united” and will “try every day to live our happily ever after”.
Klass, who has two children from her previous marriage to Graham Quinn, gave birth to her and Motson’s first child together last year.
The video shows Klass and her family sat around a table as she appears to break the news to them about her engagement to Motson.
“It wasn’t how we planned to tell our little blended family… but my daughter noticed a ring on my finger, so we decided to share some magic,” she wrote on Instagram.
Klass added: “We were having dinner and Sim quickly put his phone on record to catch them hearing the news.
“That’s why it’s a bit of a wonky shot, but it [is] also our absolute truth. He captured it perfectly.”
Klass, 42, shared the video with her 370,000 Instagram followers.
She added: “I post this as it would have been the hope that I needed once upon a time.
“It would also have been the belief that true love is out there and doesn’t always come in the most conventional of shapes or forms like the story books used to say.”
Next year, Klass is set to take a place on ITV’s Dancing On Ice.
She will be joined by celebrities including Colin Jackson, Graham Bell, Jason Donovan, Denise Van Outen, soap stars Joe-Warren Plant and Faye Brookes and DJ Sonny Jay.