Brentford said Schade had signed a five-year deal until June 2028. Financial details were not disclosed but the Athletic reported that the fee for the winger was £22 million, making him Brentford's most expensive signing.
The attacker joined Brentford in January and made 19 appearances during his loan spell, helping them earn a ninth-placed league finish.
"We have all been pleased with Kevin's contribution so far, both on the pitch and his professionalism off it, so to have him with us now until 2028 is fantastic for the club," Brentford's director of football Phil Giles said.
"We all hope both Kevin and Brentford can make further progress from here and look forward to the challenge."
Schade was called up by Germany coach Hansi Flick for friendlies against Peru and Belgium in March, making his debut in a substitute appearance against Peru before recording an assist against Belgium.
Brentford also signed goalkeeper Mark Flekken from Freiburg earlier this month.
