The Belgium international has been signed from Borussia Monchengladbach, where he spent five years – the first of which was on loan from Chelsea – and scored 46 goals in 182 appearances in all competitions.
Dortmund lost out to Bayern Munich by two points in the race to win the Bundesliga and Hazard's arrival follows that of Germany midfielder Nico Schulz, whose move from Hoffenheim was confirmed today.
Hazard had been linked with a return to Chelsea and Premier League runner-up Liverpool, but he has signed a deal with BVB until 2024 for an initial fee reported to be €25.5million.
"I am grateful for five great years and Borussia Monchengladbach and the very nice memories," Hazard said. "This was the perfect time to take the next step in my career. I am proud to play for Borussia Dortmund, a top club with incredible fans."
Sporting director Michael Zorc added: "We are delighted that Thorgan has decided to join Borussia Dortmund.
"He is a seasoned Bundesliga professional and Belgium international who will help us with his pace and finishing. He has proven his class in recent years."
Dortmund are also said to be close to signing Bayer Leverkusen attacking midfielder Julian Brandt, who is reportedly set to turn down interest from Liverpool and Tottenham to head to Signal Iduna Park.