The couple are already parents to 21-month-old Kit.
The couple revealed they were expecting their second child together in October 2016, when Sophie debuted her bump on the red carpet.
“We are expecting our second. I’m very excited,” Cumberbatch told This Morning’s Alison Hammond at the time.
“I’ll be there all the way, absolutely.”
Hammond asked Cumberbatch whether he felt being a dad was his “biggest achievement” in life.
“I think it’s Sophie’s biggest achievement,” he said. “I’m still trying prove myself as a dad.”
Cumberbatch has previously spoken publicly about wanting to expand his brood.
Shortly after the birth of his son, he said on the Graham Norton Show: “I have a new life form that needs his father’s help in the world and his mother needs a little help once in a while.
“It’s what being a parent is about, so it’s not an excuse to get away from what I am doing - it’s what I ought to be doing.
“I might go for a (Cumber)batch of boys!”
Congrats to the couple!