The Reds triggered the Hungarian's release clause to make him their second major signing of the summer.
Szoboszlai arrives, subject to a work permit, following the £35m signing of Argentina international midfielder Alexis Mac Allister from Brighton.
"It's a really historic club, really good players, good coach," he said.
"For me, it was perfect to make the next step in a club like this. The fans, the stadium, everything is really good."
The 22-year-old won the German Cup in each of the last two seasons.
Szoboszlai made 31 appearances in the Bundesliga last season, scoring six goals and registering eight assists.
He signed from Austrian side Red Bull Salzburg in January 2021 and has since scored 20 goals and had 21 assists in 91 appearances.
Szoboszlai's release clause expired on Friday but Liverpool activated it in time before agreeing personal terms.
Reds boss Jurgen Klopp is looking to reinforce his midfield with James Milner, Naby Keita and Alex Oxlade-Chamberlain leaving the club this summer.
Szoboszlai played against Liverpool in the Champions League in 2019 when he was at RB Salzburg, with his side losing 4-3 and 2-0 in the group games between them.
"We already have a little knowledge of Dominik as an opponent because we had a couple of really tough games against RB Salzburg when he was a player there, and I think everyone who saw those fixtures will have realised that even at that stage he was a really interesting prospect," said Klopp.
"I'm pretty sure he was still a teenager at that time and since then he has made some big strides - moving to Leipzig, doing really, really well in the Bundesliga, playing for the Hungary national team and then becoming captain of his national team at an incredibly young age.
"This is a signing for our present and also for our future, and the work that has gone into it could not be more appreciated."
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