Khedira, who is the younger brother of Juventus midfielder Sami, moves to Augsburg on a free transfer after making ten appearances as Leipzig finished runners-up in last season's Bundesliga.
After experiencing the upper echelons of the German top flight, the 23-year-old now hopes to help Augsburg avoid the drama of the 2016/17 campaign, in which they masterminded a four-game unbeaten streak in their remaining quartet of matches to wriggle away from the relegation zone.
"Augsburg put together an exciting run to make sure they stayed up. Now I want to help them establish themselves in the Bundesliga and take the next step in my career," Khedira said after completing his move.
"In Rani Khedira, we've been able to give ourselves a young talent with huge potential," said sporting director Stefan Reuter, after bringing in the first recruit of the summer window. "We're sure he'll be able to help the team with the qualities he has in the coming years."
The Stuttgart-born midfielder made his professional debut with his hometown club before joining Leipzig in 2014, helping them to an historic promotion to the Bundesliga a year ago.