Parker is looking forward to working with head coach Markus Feulner after agreeing a four-year contract at the SGL Arena on Tuesday.
The 21-year-old was limited to 11 appearances for Mainz last season, with Eric Maxim Choupo-Moting and Shinji Okazaki preferred in attack.
"Augsburg have a young coach, a great team, (and) a familiar yet highly professional environment," Parker told the club's official website.
"I'm sure this move is something with a lot of future prospects."
Parker's only goal for Mainz last season came against champions Bayern Munich, in a 4-1 defeat at the Allianz Arena in October.
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