The Georgian has signed a (x) year deal at Anfield but will go back to Valencia on loan this season.
Mamardashvili becomes the first signing that Liverpool have made this summer under new boss Arne Slot.
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He joined Valencia on loan from Georgian club Dinamo Tbilisi in 2021 before the deal was made permanent in 2022.
The 23-year-old made 37 appearances for Valencia last season and kept 13 clean sheets.
Mamardashvili has also earned 21 caps for the Georgian national team. He represented his nation at Euro 2024, Georgia's first major international tournament, and kept a clean sheet in their group stage win over Portugal.
He was chosen in Sporting Life's Team of the Tournament for his performances in Germany over the summer.