The Belgium international has struggled for opportunities in Edin Terzic's Bundesliga side this season, starting just two games among his 14 league appearances.
Hazard will have the chance to prove his worth to Dortmund as he joins PSV, third in the Eredivisie and trailing leader Feyenoord by four points after 19 games.
"It is a beautiful club with a beautiful shirt. PSV are still competing in the league, the cup and in Europe," the 29 year-old said. "I am really looking forward to the challenge."
PSV director of football Marcel Brands added: "Thorgan is a versatile player and he can play in several positions. He also has a lot of international experience."
Hazard, the brother of Real Madrid's Eden Hazard, could make his PSV debut in a top-of-the-table tussle at Feyenoord on Monday (AEDT).