Kevin Costner, Wife Christine Are Expecting

This will be the first child for the couple; Costner is already the father of four

Photo: Lisa O'Connor/ZUMA

Waterworld star Kevin Costner and his wife, Christine, are expecting their own little dipper, his rep said Thursday.

Christine is “doing well. She’s excited,” Costner told PEOPLE at the AT&T Pebble Beach National Pro-Am golf tournament on Friday. “I’m excited. My kids are excited.”

How is he getting ready for the baby’s arrival? Said Costner: “There’s a lot of books to read!”

Costner, 52, and handbag designer Christine Baumgartner, 32, wed at his ranch near Aspen, Col., in September 2004.

On that day, Costner arrived at the stream-side ceremony in a horse-drawn carriage, while Baumgartner pulled up soon after in a vintage green pickup truck.

The couple met while golfing more than a decade ago, but didn’t begin dating until they met again at a restaurant in 1998. Despite a brief split in 2002 and an almost 20-year age difference, the two are “like little kids together, really in love,” close friend David Giammarco told PEOPLE at the time of their wedding.

This will be Baumgartner’s first child. Costner has three adult children, Anne, 22, Lily, 20, and Joe, 19, from his previous marriage to Cindy Silva, which ended in 1994, and a 10-year-old son, Liam, from his relationship with Bridget Rooney.

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