Thiago had been linked with a move to the Reds all summer and the deal was finally completed on Friday.
The midfielder has put pen to paper on a ‘long-term’ contract on Merseyside, though will face competition for starting places.
He helped Bayern to the Bundesliga and Champions League last season though admitted he now needs a new challenge having spoken with Alonso and Philippe Coutinho.
Bayern are clearly sad to see him go, writing on social media: "Take good care of our boy #MiaSanMia”.
And former Bayern star and Reds legend Alonso replied: "Sure they will".
On needing a new challenge, Thiago said: “Because at the end, 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 am excited not just to wait to play here, but also to train with my teammates, to get to know the coach and what he wants, how the team plays.
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
“I want to help the guys if I can help them to be even better than they are, and I can be better than I am. It would be so nice and I hope for that.
“People like Philippe Coutinho and Xabi Alonso helped me a lot to take this last step. It’s really good.”