Yoo made his entertainment debut in a cellphone commercial in 1999 after Yoo's mother sent in a photo of her son to an ad agency.

In 2000 Yoo began his career as a child actor, first appearing in the television drama Daddy Fish. He rose to stardom in his first film The Way Home, playing a bratty city boy who learns to appreciate country life when he's forced to spend the summer with his deaf-mute grandmother. The low-budget film was a surprise box office hit in 2002, drawing more than 4 million admissions. He was then affectionately labeled as "Nation's Little Brother". Thereafter, Yoo also starred in animal movie Heart Is... (2006) about a boy and his beloved dog, and Unforgettable (2008) about school children from a remote island who go on a field trip to a candy factory in Seoul during the 1970s.

He continued acting in television, appearing in Magic Warriors Mir & Gaon (2005), an adventure series for children. Yoo further built his filmography, playing younger counterparts of male protagonists in television dramas, including general Yi Sun-sin in Immortal Admiral Yi Sun-sin (2004), King Seongjong in The King and I (2007), and Gwanggaeto the Great in The Legend (2007).

In 2009, Yoo starred in the action film City of Fathers and thriller film 4th Period Mystery. He also played Kim Chunchu in the period epic Queen Seondeok.

In his teens, Yoo was cast in one of the major roles in Master of Study (2010), a Korean screen adaptation of Japanese manga Dragon Zakura. He then played a more mature role in Flames of Desire, as the second-generation son of a wealthy chaebol family who is uninterested in the battles of succession among his relatives and becomes a married man at 21. Later that year, Yoo sang a duet with singer/actress IU titled "Believe in Love" for the charity program Love Request. The song's lyrics was based on a diary that Yoo had written while seeing orphans of war in the slums of Sri Lanka.

In 2011, Yoo trained in swordplay and martial arts in his role as an Assassin in Warrior Baek Dong-soo, an action-period drama based on the manhwa by Lee Jae-heon. He also voiced Greenie, Leafie's adopted son, on Leafie, a Hen into the Wild, which was adapted from a bestselling children's novel by Hwang Sun-mi. He then co-starred with Kim Ha-neul in the thriller Blind.

In 2012, Yoo was cast in his first role as a leading man in Operation Proposal, a Korean remake of the Japanese drama Proposal Daisakusen. This was followed by a supporting role as the Jade Emperor, ruler of the heavens, in the fantasy-period drama Arang and the Magistrate. Afterwards, he starred in the melodrama Missing You, playing a cold man who hides a vengeance-filled heart behind his seemingly gentle smile.

Yoo enlisted for his mandatory military Service, as a regular soldier, on March 5, 2013, where he reportedly worked training new recruits. He was discharged on December 4, 2014..

As his first post-army project, Yoo appeared in the music video for Naul's "You From the Same Time" in 2015. He was next cast as a stubborn webcomic Writer raising a cat in the TV adaptation of webtoon Imaginary Cat. Yoo followed this by starring in the joseon-era romance film The Magician directed by Kim Dae-seung, in which he plays a circus Magician who falls in love with a Princess. Yoo was then cast in SBS's legal thriller series Remember as a Lawyer with hyperthymesia who defends his father on death row.

In 2016, Yoo starred in Seondal: The Man Who Sells the River as the titular Kim Seon-dal. In 2017, he starred in MBC's historical melodrama The Emperor: Owner of the Mask and MBC's romantic-comedy I’m Not a Robot.