Yoo first met actress Kim Hyo-jin in 2003 when they were models for a clothing brand, and the two became friends after continuously meeting in photo shoots. Their romantic relationship began in 2006, and they were among the very few Korean star couples who openly admitted their dating status. They announced their engagement in August 2011, and subsequently released pre-wedding photos. Their minimalist invitation was made from environmentally friendly paper and had the number 1,825 written on it, the exact number of days the two had spent together as a couple. They were married at the Shilla Hotel in Seoul on December 2, 2011. The wedding date marked the couple's fifth anniversary together and was booked by Yoo one year in advance despite landing on a Friday – an unusual day for a wedding. The ceremony was officiated by the president of World Vision Korea; Yoo and Kim are the organization's honorary ambassadors, and they donated a portion of their monetary wedding gifts to World Vision to help build a primary and middle school in Myanmar. Their first child, a son, was born on July 5, 2014. They welcomed their second son on April 15, 2019.