PARIS—Karl Lagerfeld, the German designer who dominated high fashion for decades and reinvigorated French couture house Chanel SA as creative director, has died. He was 85, though he long refused to confirm his age.

His death leaves a void atop two fashion behemoths: Chanel, one of the luxury industry’s biggest brands, and Fendi, the Italian fashion house owned by LVMH Moët Hennessy Louis Vuitton SE where he had been a creative director since 1965. Both brands face deep questions about their future direction without Mr. Lagerfeld,...