The midfielder, 29, appeared for 15 minutes of Euro 2012 when he came on as a substitute in the 4-1 defeat to Russia.
Petrzela has now agreed to leave Viktoria Plzen in his homeland to order to complete a transfer to Augsburg, who finished fourth in the Bundesliga last season.
"I will never forget Plzen," said Petrzela. "There was a great team spirit there.
"But I have to take the next step in my career. It has always been my dream to play in the Bundesliga."
Petrzela was a member of the Plzen side who won the Czech title in 2011 and represented the club in the Champions League last season.