The 20-year-old - who made his Hammers first-team debut at the age of 16 - spent the second half of last season on loan at the Bundesliga outfit, making eight appearances.
England U20 international Oxford previously had loan spells at Reading and Borussia Monchengladbach.
"I am very happy that a solid change to Augsburg has worked out," said Oxford.
"I have felt very comfortable in the city and the club for the past six months and would now like to take another step in my development in the Bundesliga."
"We are convinced that he will strengthen us in the coming years."