The 34-year-old has already agreed the move, according to German outlet Bild, after announcing his departure from the current Serie A champions.
Lichtsteiner joined Juve from Lazio in 2011 and went on to make over 250 appearances for the Turin-based side.
During his seven years at Juve, the Swiss international won six Scudetti, three Coppa Italia titles (could soon become seven and four respectively) and also featured in two UEFA Champions League finals.
After trying to sign the Switzerland captain in 2016, Dortmund have seemingly now got their man. A deal has already been agreed and will be announced in due course.
Lichtsteiner will be a valuable asset to Dortmund as he has a great attitude and is able to get up and down the right flank tirelessly throughout every match.
However, he is no longer Max Allegri's first choice and has chosen to leave Juve. He confirmed his departure on Saturday. While not revealing the identity of his next club, he made it clear to Sky Sports (via calciomercato) that he would not join another Italian side.
"Future? I play in one of the best and biggest European clubs but I have already made up my mind. My future will be far from Juventus. Future outside of Italy? Yes but I can't say where since I haven't signed anything as of now."
According to the aforementioned report from Bild, Lichtsteiner told Swiss tabloid Blick: "I will definitely never go to China. I do not run after the money and also need to consider quality of life. My wife and children need to feel good, that would not be the case in China. And I do not need more money."