Ji, born in a small island of Chuja near Jeju Island, started his athlete career as a long-distance runner at a local elementary school. At ten, Ji was approached by a football coach from an elementary school in Jeju Island who suggested him to join the school and play football. Ji's father, who had been a volleyball player, decided to send his son to Jeju Island and thus began Ji's footballing career. Playing at Hwabuk Elementary School and Ohyun Middle School, Ji was soon recognized as a great talent and was subsequently scouted by Chunnam Dragons' U-18 team, Gwangyang Jecheol High School, which boasts one of the best youth systems in Korea. In 2007, he was sent to the youth team of English club Reading as part of a Korea Football Association's football abroad program. However, he was mostly on the bench at Reading and in 2009, he returned to Gwangyang Jecheol High School. With talented teammates such as Kim Young-Wook, Hwang Do-Yeon, and Lee Jong-Ho, Ji impressed football fans, winning numerous trophies and honors. The cream of the crop was becoming the top scorer in the High School Club Challenge League with 17 goals in 14 games in 2009.
After an impressive youth-level career, he was promoted to the Chunnam's first team before the 2010 season. He made his senior debut on 27 February 2010, starting for the first round match against Incheon United. He scored his first senior league goal on 28 March 2010 against Gangwon FC, finding the net in the 1st minute. His second came on 5 May 2010 against Chunnam's rivals Jeonbuk Hyundai Motors, again in the 1st minute. On 21 July 2010, he scored his first senior hat-trick in a Korean FA Cup match against Gyeongnam FC. In total, Ji scored 13 goals in 29 games and finished as top scorer in the Korean FA Cup in his debut 2010 season.
In June 2011, Ji agreed a deal to join Sunderland of the Premier League as a summer transfer after impressing manager Steve Bruce with his performance in the 2011 Asian Cup, in which he scored four goals and provided two assists in six games. He signed a three-year deal for an undisclosed fee (believed to be around £2 million). He made his first appearance for his new club in a 1–1 draw with Arminia Bielefeld in the club's pre-season tour of Germany. He scored his first goal for Sunderland in a pre-season friendly against Darlington. Ji made his league debut for Sunderland on 13 August 2011 coming on for Asamoah Gyan in the 66th minute against Liverpool. Ji scored his first Premier League goal in the 90th minute against Chelsea from a Nicklas Bendtner assist on 10 September 2011, to which Sunderland lost 2–1. On 2012 New Year's Day, Ji scored his second Premier League goal, a winner against eventual champions Manchester City with the last kick of the game.
On 18 May 2013, Ji scored his fifth goal of the season which led to a 3–1 victory over SpVgg Greuther Fürth, helping FC Augsburg avoid relegation. Ji finished the season with five Bundesliga goals, proving himself to be a crucial loan signing for Augsburg in their dramatic escape from relegation. The loan move was a personal success for the player, whose young career had threatened to stagnate at Sunderland. The following summer, Ji was linked with moves to a host of Bundesliga clubs.
As an international Ji has represented his native South Korea at Under-20, Under-23 and Senior level making his senior team debut in a 1–0 win over Syria on 30 December 2010 scoring in winning goal for South Korea. He has impressed during the early stages of his international career and is leading a wave of new and exciting talent pulling on the red of the national side.
Dong-won scored four goals in six games at the 2011 Asian Cup – a return which helped catch Steve Bruce's eye and seal a move to Wearside.
Ji was selected in the South Korea squad for the 2012 Olympic Games. He came on as a substitute in the three group games, and started the quarter final against Great Britain at Cardiff's Millennium Stadium, where he scored the opening goal in a 1–1 draw, with Korea progressing on penalties. Ji was selected to start the semi-final match against Brazil which South Korea lost 3–0. Ji would start again in the third place bronze medal match against Japan and played a vital role in defeating the Asian rivals 2–0. Ji ultimately earned military exemption for obtaining a bronze medal.