The 20-year-old was in demand, with Heerenveen in Holland also having an interest.
But Augsburg have concluded the deal and they will have the player for the rest of the season.
Oxford has not played for the Hammers since October 2016.
He has previous history in the Bundesliga, where he played for Borussia Monchengladbach last season.
He still has a contract with West Ham until 2021, but a permanent summer exit does seem a real possibility.