The Spain international midfielder has put pen to paper on a long-term contract with the Reds and becomes the club's second signing of the transfer window, following Kostas Tsimikas in August.
Moments after sealing the move, Thiago told Liverpoolfc.com: “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.
“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."
He added: “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 teammates, the club and also to the fans."
Reds manager Jurgen Klopp is delighted with his €30m arrival.
The German said: "Great! Absolutely great. I'm really happy that it finally worked out and we could just do it. It's very exceptional because in our situation, a lot of people around us talk constantly – 'What are you doing? – bam, bam, bam. Then preparing something like this, working on all different things you have to work in a transfer like this – with thinking about a player like him already is a joy, to be honest, because it gives us obviously some options.
"Then you get in contact with the boy and then you realise, OK, he obviously likes this project as well pretty much, even before he is here, which was really nice. I learned more and more about him as a person; the player I knew before, the person I learned. So I'm really happy to bring this wonderful person in as an add-on to the squad, which is just good for football reasons – but for all the other reasons as well. So, yeah, absolutely happy that he's here."
On what his new No6 will offer the team, Klopp also stated: "He can demand rhythm, that's how it is. He can obviously create and use space for other players, all these kinds of things. First touch incredible; vision incredible; passing pretty good! But is quick as well. Work-rate great. His numbers were absolutely special last year in Germany as well, most steals, ball recoveries and all these kinds of things; most passes. But we don't play like Bayern, so that still will need some time to get settled and nobody should expect – and I don't expect – the special things immediately, first game, let's see. It's a long-term project and we have a good team, so we can give time. But, of course, we want to use him on the pitch, that's clear. So the work can start now."