The couple first met while on the set of the 2009 two-part ITV series Wuthering Heights, in which they played the lead roles of Heathcliff and Catherine Earnshaw.
They were married five years later, and had their first child together in October 2015.
It's now been reported that Hardy and Riley have had a second child, a boy called Forrest.
According to a source close to the couple, Hardy took inspiration from the 1994 Oscar-winning film Forrest Gump when choosing the baby's name.
“They love the name Forrest as it’s earthy and strong," the insider told The Sun.
"Tom has always found the movie Forrest Gump very inspiring and enjoyable and thinks it fits.”
The insider explained that Riley gave birth to Forrest last month, but that she and Hardy decided to only inform close friends and family at the time.
“The couple are over the moon with the new addition to the family," they said.
"Friends are already saying that the baby boy looks exactly like Tom.
“They’ve been laying low over the festive period so they can get used to having a busier household and adjusting to the needs of a newborn."
Hardy had his first child in 2008, a son called Louis, with former girlfriend Rachael Speed.
The pair met on the set of The Virgin Queen in 2005, a production on which Speed was working as an assistant director. They separated in 2009 after four years together.
Following the birth of his first child with Riley, Hardy spoke to Esquire magazine about the difficulties of coping with sleep deprivation.
He explained that he started shooting his TV show Taboo three weeks after the birth, and ended up having between four to six hours of sleep every night due to "the little one".
"If anyone else did that to you you'd have them up at the Hague for war crimes," he said.