The couple - who already have three-year-old daughter Naleigh from South Korea - have welcomed another child, but a name is not yet known.
The couple's representative confirmed: ''Yes they have adopted a baby. No further details are available at this time.''
In January, 33-year-old Katherine confirmed she was talking about taking on another child with her 32-year-old husband.
She said: ''Josh and I started talking about it before we were even engaged. We have talked about having biological children as well but we decided to adopt first. I'd like to adopt again.''
The 'Grey's Anatomy' beauty previously claimed she felt like a ''bad mother'' when she first adopted Naleigh from South Korea in 2009 because she could not Bond with her.
She said: ''I fought incredibly hard for my daughter to accept me as mother. Her rejection almost broke my heart.
''At first I blamed myself and thought I was a bad mother. It took a while before I could admit to myself that the lack of trust had nothing to do with me.''