The sex and the name of the baby has not yet been released.
The 38-year-old actor and his wife only revealed they were expecting in September 2015, after Riley, 33, turned up to the Legend premiere with a noticeable baby bump.
Hardy is already dad to seven-year-old Louis from his previous relationship with Rachel Speed. This is Riley's first child.
The couple married in July 2014 after meeting on the set of Wuthering Heights in 2009.
Hardy has previously spoken out about how becoming a father made him reassess his priorities.
He told HELLO!: "Being a father has given me the kind of purpose that makes you think more carefully about how you live your life.
"I take great pride in being a father and make sure I'm there for him and helping him as he makes his way in the world."