The Magic Mike star and his wife, who married in July 2009, confirmed the news through their spokespeople, who told People.com: "They are pleased to announce that they are expecting the birth of their first child next year."
The 32-year-old actor, who was crowned People's Sexiest Man Alive of 2012, recently teased that the couple - who met on 2006 dance film Step Up - were getting broody.
"I'm ready; I think she's ready," he said.
Channing - who has four films out next year, including the GI Joe sequel and Steven Soderbergh's psychological thriller Side Effects - also hinted that they may not stop at one child.
"The first number that pops into my head is three, but I just want one to be healthy and then we'll see where we go after that," he said.
"It's really easy for us guys to say, 'I want like 15 kids'. Jenna will be like, 'Well you better get another wife!'" he joked.