Liverpool will pay £20m for the Spain international, Thiago Alcantara with the potential for a further £5m in add-ons, and the midfielder will wear the No 6 jersey.
The 29-year-old helped Bayern win the treble last season, as they beat Paris Saint-Germain in the Champions League final last month in Lisbon.
“I think it’s an amazing feeling. I was waiting for this moment for a long time and I am very, very happy to be here,” Thiago told Liverpool’s official website.
“When the years are passing, you are trying to win as much as you can – and when you win, you want to win more. I think this club describes what I am as well; I want to achieve all of the goals, win as many trophies as possible.
“It also has this kind of family feeling that I need because we like to have a very close relationship with the club and I think I will feel this, I will have this feeling, with this club as well.
“I must adapt to the team as fast as I can in the situation and the context that we are living right now.
“Everything is more compact and we started a little bit later, but still it is football and I think we have to mix all the big things up, all the good things we have. I will help the team in a defensive and offensive way and also in a mental aspect.
“The fans are not more excited than I am – for sure not! It is not about saying words, it is about doing the things. I will give my heart on the field to my team-mates, the club and also to the fans.” – Agency report.