Liverpool have signed midfielder Thiago Alcantara from Bayern Munich on a four-year deal for £20m.
The fee for the Spain international, 29, could eventually rise to £25m with bonuses.
"It's an amazing feeling. I was waiting for this moment for a long time and I am very happy to be here," he said.
Thiago will wear the number six shirt at Anfield and becomes the club's second summer signing after Greece left-back Kostas Tsimikas.
He will be eligible to play against Chelsea at Stamford Bridge on Sunday.
Thiago won La Liga twice with Barcelona before a 2013 move to Bayern, where he won the Bundesliga seven times and the Champions League in August.
His arrival at Anfield ends weeks of speculation about whether the Premier League champions would make a stand-out summer signing.
The £20m fee will be paid in instalments over the length of the deal, and up to an additional £5m will be paid based on the Reds' success in the Premier League and Champions League as well as any individual awards earned by Thiago.
"Absolutely great - I'm really happy that it finally worked out and we could just do it," said Liverpool manager Jurgen Klopp.
"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."
Thiago 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."
Klopp said: "When we spoke about all the players, he respects them all massively. He admires them.
"We played against him when we played Munich in the Champions League two years ago [Liverpool won 3-1 in the second leg of their last-16 tie after a 0-0 draw at Anfield], so he knows what kind of machine we can be and he wanted to be part of that."
Meanwhile, Liverpool have targeted another addition in Wolves forward Diogo Jota, who was a surprise omission from his side's Carabao Cup defeat by Stoke on Thursday.
After the game, Wolves manager Nuno Espirito Santo repeatedly refused to state the reason for the Portuguese's absence.
Now it has emerged the 23-year-old former Porto and Atletico Madrid player is being targeted by Klopp's side in a deal that could be worth up to £35m.
Jota joined Wolves on loan in their 2017-18 Championship-winning campaign, making a £12.8m permanent switch in 2018. He has made 131 appearances, scoring 44 goals, including hat-tricks in last season's Europa League victories against Besiktas and Espanyol.
Any deal, which would represent a record transfer sale for Wolves, is likely to see full-back Ki-Jana Hoever move the other way.
The 18-year-old Dutchman can play either as a full-back or in central defence and fits Wolves' recent quest to bring in younger players they can develop.
Analysis - 'Thiago one of best midfielders in the world'
The Athletic's Raphael Honigstein on Radio 5 live's Euro League's podcast
It [the Thiago deal] is quite cheap considering what you are getting, which is one of the best holding midfielders in the world.
Liverpool fans should consider themselves very lucky because they are picking up an absolute superstar who could probably play in any team in the world. They have plenty of reason to be excited.
When Pep Guardiola went to Bayern, his first signing was Thiago and he said 'it's Thiago or no-one for me'. When Thiago got injured he then went to buy Alonso as a replacement.
Thiago is in the form of his life, the way he played in the Champions League, combining that skill and elegance with winning balls back.
He makes it look effortless. It adds something to that Liverpool midfield, which doesn't quite have that skill-set. The idea is to rotate a lot more. There will be so many games - this will be the shortest, most insane season ever - so to rotate players around is going to be brilliant for a team who play with so much energy.
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