Adrian was a free agent after leaving West Ham at the end of last season and moves to Anfield on a two-year deal with the option for a third.
Adrian’s arrival continues a relatively quiet transfer window for Liverpool, whose other incomings this summer include teenagers Sepp van den Berg and Harvey Elliott.
"I'm feeling really happy; really happy to be here and to work in this great club and start doing my stuff on the pitch as soon as possible," Adrian told Liverpoolfc.com.
"I'm very ambitious, I come here to try to win everything, to try to push Ali from the first minute and to make us better.
"Obviously I want to win titles. I come here to fight for all the competitions. We have many competitions ahead - we're going to fight for it and try to get them."
Mignolet left Liverpool for Club Brugge after warming the bench in Sunday’s Community Shield penalty shootout loss to Manchester City, with the European champions receiving a £6m fee for his transfer.
Adrian will serve as a replacement for Mignolet and a back-up to Alisson Becker.
The 31-year-old Spaniard had been on the books of West Ham for the last six seasons, making 150 appearances in all competitions for the Hammers but lost his place to Lucasz Fabianski last season.
