A rep tells us the two recently welcomed a baby girl ... a source with knowledge of the new addition tells us the "Game of Thrones" star gave birth to the couple's second daughter earlier this month in Miami. We're told Sophie and the newborn are home from the hospital and relaxing.

We broke the story ... the couple welcomed their first daughter, Willa in July of 2020 in Los Angeles ... shortly after they tied the knot in 2019 during a Las Vegas wedding.

You'll recall, Joe and Sophie moved from the west coast to Miami last year where they scooped up an $11 million waterfront mansion. Seems like the south is treating them well!