Bobadilla, who joined Gladbach in 2009, has failed to earn a regular starting spot and has mainly been a substitute in the current campaign in which the team have climbed to fourth place, just a point behind leaders Bayern Munich.
"In the second part of the season it would again be difficult for Raul to get starting spots so the transfer at this moment makes sense," said Gladbach sports director Max Eberl.
The 24-year-old Argentine joined Gladbach from another Swiss side, Grasshoppers, before a short loan spell at Aris in Greece.
No details of his contract with Young Boys were released.
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