Speaking with Entertainment Tonight, the 55-year-old actor said he became "a real dad teary" seeing how much his daughters have grown up.
"They're all having fun while I'm working, but I'm so happy they're here," Damon said. "Everybody's so grown up."
Damon shares three daughters—Isabella, 20, Gia, 17, and Stella, 15—with his wife, Luciana Damon. He is also stepfather to Luciana's eldest daughter, Alexia, whom she had before the couple married in 2005.
In a previous interview with PEOPLE, Damon said his family enjoys traveling together, often joining him while he works overseas. He said many of them will accompany him on the international promotional tour for The Odyssey, with stops planned in Europe, Mumbai, Beijing, and Seoul.
Directed by Christopher Nolan, The Odyssey stars Damon as the Greek hero Odysseus. The film opens in theaters on July 17.
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