The pedigreed midfielder passed a medical on Friday before penning a four-year deal with the champions of England.
“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,” said Thiago. “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.”
The Merseysiders had been in talks with their Bundesliga counterparts from the start of the week over structuring the fee, with an agreement between the clubs materialising on Thursday morning.
A guaranteed £20m will be paid over the course of Thiago’s contract, while an additional £5m is dependent on performance-based bonuses, such as winning the top flight or Champions League.
Progression through the rounds in the latter competition would also count if the player is integral to Liverpool’s success while individual honours also count towards it.
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.”
Thiago will wear the No 6 shirt at Anfield and arms Klopp with greater tactical variety, press resistance as well as unique passing ability.
“Thiago is an extraordinary player and was very important for us,” said Bayern coach Hansi Flick. “It was a joy working with him.
“Thiago gave the team a lot of options and made us unpredictable, he solved things in ways you don’t expect. I congratulate Klopp — he gets a top player and a sensational person.”
Liverpool have also been scouting a forward option with Watford’s Ismaila Sarr one of the candidates being assessed, but his £40m valuation is prohibitive.
The club are short at centre-back after Dejan Lovren’s departure, but the signing of Thiago allows Klopp to drop Fabinho in the heart of defence if needed.