Endo has been signed for £16m from the German Bundesliga side on a four-year contract after Liverpool missed out on both Moises Caicedo and Romeo Lavia to Chelsea.
Liverpool needed to reinforce in midfield after Jordan Henderson and Fabinho moved to the Saudi Pro League and Naby Keita and Alex Oxlade Chamberlain departed at the end of their contracts this summer.
The 30-year-old, who arrives on Merseyside after four seasons at Stuttgart, where he made 133 appearances and scored 15 goals, told the club's website: "I'm very happy right now and I'm so excited to join a big club in Liverpool.
"It feels amazing and this is my dream. 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.
"It's going to be the first time for me that I play at Anfield. I can't wait to play at Anfield in front of Liverpool fans.
"I play as a No 6 and I'm like a bit more [of a] defensive player. I think I can help this club defensively and I will have good organisation in the middle. I think that's my job."
Endo captains the Japanese national team.
"I'm really happy. Wataru is a really good player," Liverpool manager Jurgen Klopp said. "I know in this world of football how it goes and stuff like this, but have a look, have a look, because he's a really good player.
"Experienced player, captain of Stuttgart, captain of Japan, speaks good English, nice fella, family man, machine on the pitch, good footballer on top of that, sensational attitude. So, I'm really happy. He's a good footballer, very experienced and loves to work extremely hard."
Endo has been handed Fabinho's number 3 jersey.
