Goran Visnjic, who plays ER's Dr. Luka Kovac on the long-running NBC medical series, and his wife, Croatian artist Ivana, have adopted a baby boy whom they've named Tin Visnjic, the actor's rep tells PEOPLE exclusively.
The baby was born on April 19 at Cedars Sinai Medical Center in Los Angeles.
This is the first child for the couple, who married in 1999.
Speaking to PEOPLE in 2005, the 6'4" Visnjic, now 34, said of being ER's resident hunk (he joined the show in 1999, succeeding George Clooney), "I wouldn't know about that. If that's the case, it doesn't have anything to do with me. It's genetics. [Thank] my parents."
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