The Hollywood couple reportedly welcomed the baby over a month ago, but are yet to publicly announce the arrival.
The lovebirds — parents to daughters James, four, and Inez, two — revealed they were expecting another bub at the May premiere of Pokémon: Detective Pikachu.
Lively, 31, posted a joyous picture of the pair on the red carpet which showed her resting one hand on her belly, with the caption “PokeMOM… Out now”.
The actors have yet to share details of the birth, however a source told US Weekly the baby “is about two months old”.
While the baby’s name or gender hasn’t been revealed, Reynolds told PEOPLE in 2016 that “if I could have nine daughters, I would be thrilled. Really, like I genuinely would be”.
In April this year, Reynolds gushed to cable TV show Extra that when his children “decide to go away to college… I’m going to be so needy”.
“I love being around them — it’s the best thing in the world.”
The couple met on the set of Green Lantern in 2010, when they were both in relationships — Lively was dating Gossip Girl co-star Penn Badgley and Reynolds was married to actress Scarlett Johansson.
They reportedly started dating around a year later in October 2011, and were married in September 2012.
The famous couple are fiercely private when it comes to their children, keeping them largely off social media.