Barker commented with a black heart emoji and posted the same picture to his Instagram Story.
They had both previously hinted at their relationship on social media and posted pictures of the same fireplace on Valentine’s Day.
Kardashian has three children with ex-partner Scott Disick while Barker, an acclaimed drummer and music producer, is a father of two.
He was been married twice, including to former Miss USA Shanna Moakler.
Kardashian will appear in the final series of her family’s reality TV show when it airs in the US next month.
A trailer for series 20 of Keeping Up With The Kardashians teased her and Disick asleep on the same sofa, leading her sister Kendall Jenner to say they are “made for each other, they’re supposed to be together”.
Kourtney Kardashian and Blink-182 star Travis Barker make it Instagram official