Lehmann was part of Arsene Wenger's backroom team at Emirates Stadium but left the club after the arrival of Unai Emery last year.
He joins Tobias Zellner, Michael Wimmer and Jonas Scheuermann in Manuel Baum's coaching team at Augsburg Arena.
"Augsburg have developed incredibly in recent years," Lehmann told the club's official website. "This is a brilliant opportunity for me to work as an assistant coach in the Bundesliga and to help the players reach their potential on the pitch."
Baum is thrilled to be adding Lehmann to his staff, with his side 15th in the Bundesliga having drawn three and lost seven of their last 10 league games and just a point out of the relegation play-off spot.
"I am delighted to announce that Jens Lehmann will join the club as an assistant coach," he said. "He is an expert of the game, who possesses a lot of experience. I look forward to working with him and I'm sure he will enhance our team and our work on and off the pitch."
General manager Stefan Reuter added: "A coaching team has to work on so many diverse and thorough tasks. Therefore, we came to the conclusion that we wanted to expand our coaching team to specialise into different activities.
"Appointing Jens Lehmann is absolutely incredible! He will work alongside Manuel Baum to develop our squad each day both on and off the pitch."
The former Gunners keeper spent the majority of his career in Germany, playing nearly a decade with Schalke. After a brief spell with Milan, Lehmann returned to the Bundesliga with Borussia Dortmund, where he played four seasons.
After his five years with Arsenal, which included being part of the club's "Invincibles" in his debut season, Lehmann returned to Germany with Stuttgart before finishing out his career with a lone appearance for Arsenal in 2011.