London: Liverpool signed Spain midfielder Thiago Alcantara from Bayern Munich for a reported fee of £20 million ($26 million) on Friday.
Thiago agreed a "long-term contract" with the Premier League champions after deciding to end his seven-year stay with Bayern.
The 29-year-old moves to Anfield after helping Bayern win the Bundesliga, the German Cup and Champions League last season.
"I think it's an amazing feeling. I was waiting for this moment for a long time and I am very happy to be here," Thiago told Liverpool's website.
It is believed Thiago has penned a four-year deal with the Reds, who had been tracking him for several months and could pay Bayern another £5 million in add-on bonuses.
Thiago will wear the number six shirt at Anfield and becomes Liverpool's second signing since the end of last season after Greece left-back Kostas Tsimikas.
Thiago joined Bayern from Barcelona as Pep Guardiola's first signing in 2013 but with a year left on his contract he had stalled over signing an extension and decided to try a new challenge.
He enjoyed a trophy-filled stay in Germany, winning seven Bundesliga titles, four German Cups, the Club World Cup and the Champions League last month in Lisbon.
Now Thiago believes he can enjoy similar success with Jurgen Klopp's side.
"When the years are passing, you are trying to win as much as you can and when you win, you want to win more," Thiago said.
"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 with this club as well.
"I will give my heart on the field to my teammates, the club and also to the fans."
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Liverpool face their first challenge without Van Dijk in Wednesday's Champions League group match away at Dutch side Ajax.
Borussia Dortmund needed substitutes to dig them out of a hole for a 1-0 win against Hoffenheim, while Bayern Munich had no such difficulties as they romped to another Bundesliga rout on Saturday.
Van Dijk was on the end of a shocking challenge from Everton goalkeeper Jordan Pickford in Saturday's 2-2 draw in the Merseyside derby