The Reds were forced to wait to announce the addition due to paperwork and registration issues, but his signing has now finally been sealed, ending their search for a left-sided defensive option.
The Frenchman, 20, joined the Bavarian giants from ES Troyes AC and played 25 times for Bayern's second team last term, scoring twice against in 3.Liga
So far this season, the 20-year-old has made two appearances in the Regionalliga Bayern.
Vita joins on loan for the rest of the season, with the Reds having a purchase option.
Barnsley FC co-chairman Paul Conway said: “It’s no secret that as a club, we identify young, hungry individuals who both want to play for Barnsley FC and progress in the game.
"Rémy meets that criteria, and arrives at Oakwell with a determination to improve and provide quality on the left-side of Markus Schopp's team.
“We are proud of the evolution of our club. It is significant that we can now sign players and are entrusted by two of the best clubs in world football, Bayern Munich and Manchester City.
“We look forward to Rémy linking up with the rest of the squad following the international break.”
Vita will provide competition for the likes of Ben Williams and Liam Kitching and his arrival follows on from the deadline-day loan capture of Claudio Gomes.