Wataru Endo has played a key role in keeping Stuttgart in the Bundesliga for the past three seasons
The 30-year-old Japan international has agreed a four-year contract.
Liverpool have brought in Endo after missing out on Ecuador international Moises Caicedo and Belgian midfielder Romeo Lavia to Chelsea.
Endo can also play at centre-back but has been signed primarily as a central defensive midfielder.
"It feels amazing," he said. "It's always been a dream to play in the Premier League and with one of the biggest clubs in the world. It's a dream come true for me.
"I think I can help this club defensively and I will have good organisation in the middle."
The signing of Japan captain Endo, who was also Stuttgart's skipper, follows the departures of midfielders Fabinho, Jordan Henderson, James Milner, Naby Keita and Alex Oxlade-Chamberlain from the Reds this summer.
Liverpool boss Jurgen Klopp has already secured reinforcements in the middle of the park, with new purchases Alexis Mac Allister and Dominik Szoboszlai starting the opening 1-1 draw with Chelsea at Stamford Bridge on Sunday.
"I'm really happy. Wataru is a really good player," said Klopp. "He is very experienced and loves to work extremely hard.
"He's a late bloomer, he was definitely underestimated, but he has improved every year since he has been in a proper football setting.
"When he came to Stuttgart he got an opportunity and never gave it away. When I saw him there's no chance I thought he was 30.
"On the pitch, he's a monster and wants to fight. He has been on my radar for a while. I'm personally really happy and now let's start working."
Endo, who has 50 caps for Japan, joined Stuttgart initially on a season-long loan in 2019 from Belgian club Sint-Truiden before the deal was made permanent a year later.
"Both in sporting and in human terms, we're losing a very reliable player and captain in Wataru," said Stuttgart manager Sebastian Hoeness.
"The important goals he scored are only part of the reason why he's been so significant for us.
"The fact that he can fulfil his dream of playing in the Premier League at the age of 30 is also recognition for the club and the people who have accompanied him here. I wish him all the best."
-- Courtesy of BBC Sport