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.
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.
"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.
