The 21-year-old forward requested the move with Mainz obliging following an approach from the Bavarians.
"Shawn approached us because he felt he needed a change. He wanted to play a more important role in a new environment and in a new team than was possible with us recently," said Mainz's sporting director Christian Heidel. "We think this step is a good decision for his personal development and we therefore wish him all the very best."
Parker was a produce of Mainz's youth academy and he made his Bundesliga debut in October 2012 against 1899 Hoffenheim. He totalled 27 Bundesliga appearances for the Coface Arena club, scoring four goals, although he made only three starts last season.
"Augsburg have a young coach, a great team and a tight-knit yet highly-professional environment," said Parker. "I'm sure something big is growing here in terms of the future and to be part of it is a big opportunity which I am delighted to take."