The 20-year-old, who was part of the South Korean squad that finished third in the Asian Cup in January, would travel to Sunderland to complete a medical before the end of the month, the Dragons said on their website.
"Ji Dong-won's transfer will inevitably leave a big hole in our roster. But for the sake of the player's future and for the development of Korean football, we decided to allow his move," a statement said on Wednesday.
The Dragons said the player would sign a three-year contract with Sunderland, who finished 10th last season after a disappointing run towards the end of the season, but did not reveal the transfer fee.
South Korean media estimated the fee would be 3.8 billion Korean won ($3.5 million) for the player, who will look to match the achievements of compatriots Park Ji-sung at champions Manchester United and Bolton Wanderers's Lee Chung-yong.
Ji is currently with the South Korean under-23 squad preparing for the second-leg of their 2012 Olympic qualifier against Jordan on Thursday. The Koreans lead 3-1 from the first leg.
"I had the impression that Sunderland really wanted me," the Yonhap news agency quoted Ji as saying.
"I know there will be stiff competition for playing time, and my goal is to become the player that the team wants me to be in six months. I am also looking forward to playing against Ji-sung and Chung-yong, whom I both admire."
If he completes the move Ji will compete against Frazer Campbell and Ghana's Asamoah Gyan for a place in attack for Sunderland.
The Korean has looked impressive with his technical ability and eye for goal at international level where he has scored six times in 11 appearances.
