06/25/2014 at 07:20 PM EDT
These days, Eric Dane
is all about family.
The star of this summer's hit TNT drama The Last Ship
cherishes his life at home in L.A. with his wife of nearly 10 years, actress Rebecca Gayheart, and their two daughters, Billie
, 4, and Georgia
"I honestly think I'm exactly where I'm supposed to be at this moment in time," the actor, 41, tells PEOPLE. "And I'm really happy."
But the road to humble family man wasn't an easy one. In 2009 a leaked video
of Dane, Gayheart and another woman hit the Internet. Two years later, the actor went into rehab
for an addiction to painkillers following a sports injury, but Dane is certain about those issues being problems of the past.
"We've all made mistakes. My one regret is that I got the person I love most wrapped up in all that: Rebecca," Dane says candidly.
The actor – who became a household name after his famous shower scene on ABC's Grey's Anatomy earned him the nickname
"McSteamy" – is embracing his latest role on Ship
, but it's at home with his family where he feels happiest.
"I never had a family, and now I do," Dane, whose father died when he was 7, tells PEOPLE. "I know I'm a very lucky guy."
For more from Dane on his career and family life, pick up the latest issue of PEOPLE, on newsstands Friday