The 30-year-old spent the second half of last season on loan at PSV Eindhoven, representing the Dutch side on 13 occasions in all competitions, scoring twice and providing one assist.
Hazard has now departed Dortmund on a permanent basis, ending his four-year association with the club.
The Belgium international represented BVB on 123 occasions in all competitions, scoring 18 goals and registering 21 assists, helping the club win the DFB-Pokal trophy.
Anderlecht have picked up 13 points from their first six matches of the new Belgian season to sit second in the table, level on points with leaders Gent.
Hazard's debut for his new club could potentially come against Kortrijk on September 17.
"I am very happy to sign for Anderlecht. I also felt like returning to Belgium with my family," Hazard told the club's official website upon confirmation of his move.
"I had been following the developments at the club closely all summer and I was impressed by the mercato, the quality of the squad and the project of the club.
"I really wanted to be part of it, and I am looking forward to getting to know everyone and rediscovering the Belgian league."
Meanwhile, CEO Jesper Fredberg added: "We have big ambitions for the future. Bringing Thorgan Hazard here is another proof of that.
"Thorgan is Belgian, experienced, and he fits the profile that we were looking for: he's technically skilled, offensive and yet also has that physical and aggressive aspect to his game.
"Above all he is still extremely hungry to achieve success with us. We're looking forward to building the future together with this squad."
Hazard started his professional career with Lens in 2011, while he also represented Chelsea and Borussia Monchengladbach ahead of his switch to Dortmund.