The France international cost Bayern Munich €41.5 million, with a five-year-contract agreed by the midfielder.
Tolisso primarily plays in midfield, but has shown how versatile a player he is after breaking into the first team at Lyon.
Tolisso expressed his delight at signing for Bayern, and also thanked his former club.
“I had a wonderful time at Lyon, and I’m very thankful for that,” he told Bayern Munich’s official website. “Now I’m really pleased to be at one of the best clubs in Europe. I have great aims for my time at FC Bayern. Today is a great day for me.”