Jennings has signed a three-year contract with the Reds after the two clubs agreed a fee of £250,000 for the 20-year-old.
"I spoke to the manager and the assistant manager and they outlined the plans they had for me and I felt Barnsley was the right club to take me further," Jennings told Barnsley's official club website.
"My time at Bayern Munich has given me a different experience and I have learned a lot from it which I can bring back here.
"It's a great opportunity for me to play football back in England where I want to be and at a high level with a club that has great plans for this season.
"You only have to look at the second half of last season to see that Barnsley would have been in the top six based on those results, so it is very exciting.
"I can't expect to turn up and play every week. I will have to work hard and do well for the team to earn the opportunity."
Jennings came to prominence for Tranmere during the 2010/11 season when he won the League One Apprentice of the Year award and spent two seasons at Bundesliga champions Bayern after leaving Prenton Park in 2011.
But he endured an injury-blighted two seasons at Bayern and failed to establish himself in their first-team squad.
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