Germany's Bild newspaper reported that the fee for the Paraguayan striker, who has agreed to a four-year deal with the Chinese Super League club, is believed to be around 12 million euros.
Barrios was a key player in Dortmund's run to the Bundesliga title last season, finishing top of the club's scoring charts with 16 goals.
However, the forward picked up an injury at last summer's Copa America and duly missed the start of this season. Since then he has fallen down the pecking order in Jurgen Klopp's side who clinched the title again last month on the back of Robert Lewandowski's goals.
Barrios was thought to be on his way out of the club in the January transfer window with a number of European clubs interested, but a move to Fulham reportedly fell through.
"Lucas Barrios won two championships for us and scored 39 goals in 82 league matches for Borussia. Therefore, we want to acknowledge Lucas' merits and meet his wish to change club in order to play again regularly," Dortmund director Michael Zorc revealed.
Barrios is now set to join former Chelsea striker Nicolas Anelka, currently at Shanghai Shenhua, as one of the marquee stars in the Chinese Super League. He will play alongside Argentine midfielder Dario Conca at Guangzhou.