Paltrow is now engaged to Brad Falchuk; he turned 47 on March 1.
She shared a shirtless picture of Brad, along with the caption: "Happy birthday - you are the grounding force, the epitome of love and kindness. Thank you for being my beacon."
Martin is dating now Dakota Johnson, 28.
Paltrow recently told "Entertainment Tonight" that while the exes have remained on friendly terms since their high-profile split, it hasn't always been easy.
She said: "I think that's probably a big misconception about me or my life that things come easily or are easy, and it's just not true.
"It's been really a process to get to the point where we can all be together and luckily I have a deeply loving ex-husband, who's very open minded, and we've been able to create something. It's for the kids. You don't want your kids to suffer."
And Gwyneth admitted that, in a perfect world, she would have remained married to Chris.
The actress explained: "Obviously if I could have stayed married to the father of my kids, that's kind of the dream, but it didn't work out for me. So you have to adapt and learn, learn your lessons and move on, and that's what we're trying to do."
