Gadou, 19, arrives from Red Bull Salzburg on a deal running until 2031 for a reported fee of 20 million euros (£17.35 million) plus bonuses.
A France international at junior levels, Gadou came through the Paris Saint-Germain academy before moving to Salzburg in 2024.
The transfer is Dortmund's first under new sporting director Ole Book, who pledged to return the club's focus to signing young talents.
Erling Haaland and Karim Adeyemi also joined Dortmund from Salzburg.
Sule, a 49-time Germany international, announced earlier in May that he would retire in the summer, aged 30.