The 44-year-old star had alerted fans to his marriage during an appearance on the Inside of You podcast last month.
He said: “I’m beyond grateful for my family and my kids and my wife.”
Throughout the conversation, podcast host Michael Rosenbaum continually referred to Kongsved, 33, as the Yellowjackets actor’s “wife” as well.
Wood has made a concerted effort to keep his personal life out of the spotlight over recent years and the birth of his second child only emerged over a year later when he mentioned his daughter in an interview.
Asked about his average day, WoodElijah told the Wall Street Journal newspaper in July 2023: “We’ve got a 3-year-old son and a 14-month-old daughter, and she wakes us up pretty early. I like getting up early, I like starting the day.”
The movie star and his kids always eat breakfast together, with Wood serving them “oatmeal with various spices, peanut butter and fruit – banana, apples, blackberries. I also really like overnight oats or muesli with yoghurt, and I sometimes eat that with them”.
He also told how he has a private Instagram account so he can share pictures with his friends and family only.
Speaking about his approach to social media, he told the Wall Street Journal: “I wanted to be able to share photos that I didn’t necessarily want to share with the world. An account that’s public-facing would really change what I share.
“It’s not like I’m sharing anything that I wouldn’t want to go out, but I’m a relatively private person.”