Liverpool have completed the signing of Bayern Munich midfielder Thiago Alcantara on a four-year contract.

The Spain international, who was in the last year of his deal with the Bundesliga club, arrives for an initial fee of £20m.

Thiago admitted he has been waiting a long time for his move to Liverpool to go through.

"I think it's an amazing feeling," he told liverpoolfc.com. "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."

Liverpool manager Jurgen Klopp said: "I know all the people at Bayern wanted to keep him desperately, that's normal and understandable because he played an important role, in the last season as well.

"He just was ready for a new challenge and he decided for us.

"It is about the club, it’s about the team, that he wanted to join us. That’s really cool.

"I thought a lot about him but never as a potential transfer, to be honest."

Earlier this morning, Thiago had bid an emotional farewell to Bayern ahead of his move to Anfield.

In a video on Twitter he said: "I have made the most difficult decision of my sports career.

"I will close this chapter on this wonderful club where I have grown as a player for seven years. Triumphs, joy and also hard times.

"But what I am most proud of is that I arrived in Munich as a young man filled with dreams and now I will leave completely fulfilled with a club, a history and a culture.

"My decision is purely of a sporting nature. As a soccer player I want new challenges to develop myself further."

Meanwhile, Klopp has not ruled out making further signings before the end of the transfer window to add to the arrival of Thiago.

And the signing of the 29-year-old playmaker does not mean players will have to be offloaded.

Georginio Wijnaldum has been heavily linked with Barcelona to link up with his former Netherlands manager Ronald Koeman and there was a school of thought that there would have to be a departure before there could be an arrival.

Klopp has dismissed that, however, and insisted there had not been a change in transfer policy. That could mean more arrivals with Watford's Ismaila Sarr and Wolves forward Diogo Jota also believed to be in the club’s sights.

"It’s just about timing," said Klopp. "Sometimes you buy before you sell, sometimes you sell before you buy. Sometimes different scenarios.

"Sometimes you don’t buy now but you buy later and sometimes you earn the money back in different ways.

"The only thing which is always true with us is what we earned on football, we spend on football. That is the short summary of the philosophy of the club. One of the key points.

"We cannot just say 'This year we need this and that, and we cannot afford it’ – and I wouldn’t insist on it.

"But this season we worked constantly on improvement. The window itself leaves the window open.

"I cannot promise we will do something and I wouldn’t but I cannot say it is 100 per cent sure we don’t do anything.

"It’s the situation, it is developing a situation so anything could happen. If a player comes to me and asks me ‘Boss I want to go’ – I don’t expect that but it can happen – then we have to react."

Thiago is Liverpool's second recruit in the close season, a stark contrast to Sunday's opponents Chelsea, who have spent more than £200m on half a dozen new signings as Frank Lampard rebuilds his squad.

Although Klopp recently said Liverpool were different from "clubs owned by countries and oligarchs", he maintains he has no problems with how Lampard and Chelsea do their business.

"There is no rivalry. You make a story that I said something about the transfer business of Chelsea," Klopp said.

"What I said is that in the situation we're in, we cannot deal with the situation like other clubs - one of them was Chelsea. I respect a lot what he is doing."

Hakim Ziyech, Ben Chilwell and Thiago Silva will all miss the clash at Stamford Bridge.

The new recruits must wait for their league debuts for the Blues, with Ziyech still nursing a knee complaint, Chilwell a heel issue and Silva searching for match fitness.

Christian Pulisic is still to shake off a hamstring problem, but striker Timo Werner is fit, having eased past a dead leg picked up at Brighton on Monday.