"We are delighted to have signed one of Europe's most sought-after talents with Xherdan Shaqiri," said sports director Christian Nerlinger in a statement.
The pint-sized 20-year-old, who will officially join from July 1, signed a deal until 2016.
"Xherdan will strengthen our team from next season with his football intelligence and dribbling", said Bayern coach Jupp Heynckes.
"I have been watching him for some time and I am convinced he can become an important player for the club."
Bayern take on Shairi's Basel in their Champions League round of 16 later this month.
'I think everybody has said something about it, so why should I add to it? It's so obvious that it's not necessary for me to' Everything that Liverpool boss Arne Slot said about James Tarkowski's unpunished horror tackle
Gary Lineker unveiled as FourFourTwo's latest cover star - we sat down with the legend of football and broadcasting to discuss his future after BBC Match of the Day
