The NCIS actor and wife Bojana Jankovic welcomed a baby girl, their second child, on Tuesday (April 10).
Talking to People, Weatherly said that Jankovic had chosen the name Olivia as it was deeply connected to her own.
"My wife Bojana is Serbian and her name means war or warrior," the 43-year-old explained.
"And when you give someone an olive branch, that's an offering of peace so Olivia is peace. I think we have a Tolstoy novel going on now: Mother and daughter, war and peace!"
Weatherly also expressed his excitement at being able to share his daughter's arrival with his NCIS castmates, adding: "I instantly felt surrounded by the love. I got a big hug from Mark Harmon. I was of course texting everyone! Everyone here has been incredibly supportive."
He and Jankovic originally announced the pregnancy in January.