The couple, who generally keep their relationship very private, have kept the news about the baby son close to their chests until recently when Sam revealed that he would be spending Father's Day with his wife and baby son.
Sam revealed the couple share a baby boy
He told People magazine: "I'm filming so much at the moment, I don't get the opportunity to spend as much time with him as I'd like to. So I think after Me Before You finishes - which is just before Father's Day - I will have a bit of family time.
"Just with the little man. I don't know what to expect - I have no expectations. I've never had that to look forward to before. I always thought, naïvely, that I knew what it would be like. I always thought that I'd understand. But it's like another level of love that you've never experienced before."
He continued to chat about his six-month-old son, saying: "You can't describe to someone unless [they’re] in it…The rewards are just endless. He's literally the best thing that's ever happened to me."
Laura gave birth in December
The Hunger Games actor is currently promoting his latest release Me Before You, which sees him play a quadriplegic with limited movement who is cared for by Louisa, played by Emilia Clarke.
Speaking about the challenging role, Sam told EW: "I think playing Will was undoubtedly probably the most challenging thing I've ever done in my life. I honestly was an emotional wreck pretty much the entirety of the film.
"One of the hardest and most challenging things about this job was actually keeping a straight face during the scenes in which our characters weren’t meant to like each other. I had a fake beard on, and all I remember is sort of trying to hold it down because every time I'd smile, it would pop off."