Forward Rebic moves to the 2. Bundesliga side on loan, while centre-back Compper's switch to the Red Bull Arena is a permanent one.
They join a Leipzig side that will be aiming to continue their charge up the German football pyramid following promotion to the second tier last season.
Compper has signed a contract with Leipzig until June 2017, bringing to an end an 18-month spell with Fiorentina.
The 29-year-old made 26 appearances for the Florence club, scoring one goal.
Meanwhile, Croatia forward Rebic will hope to gain further experience after playing in just five games last term.
The 20-year-old played in all three of Croatia's matches at the 2014 World Cup, but failed to find the net.
Leipzig began the new season on Saturday with a 0-0 draw against Aalen.
