The 24-year-old has failed to become a regular at Borussia Monchengladbach since joining the club in 2009.
Gladbach’s sports director Max Eberl said: “In the second part of the season it will be difficult for Raul to get starting spots so the transfer at this moment makes sense.”
Bobadilla joined Monchengladbach from Swiss side Grasshoppers Zurich in 2009.