Following the £8 million departure of Simon Mignolet to Club Brugge, free agent Adrian has been signed by Liverpool in order to provide backup for Allison.
Adrian, 32, completed is move to Anfield following successful medicals and having reached a consensus on personal terms with the club on Monday. The contract, according to sources, will last for two years with the option of an extra year.
"I think this is the perfect solution for us in this moment, replacing talent and experience like for like," Liverpool boss Jurgen Klopp said of Adrian "With Ali and Simon, I felt like we had two No. 1s and in many ways we have repeated that with Adrian.
"This is important. He is a 'keeper who knows the Premier League, who has played in pressure situations and has the highest quality.
"They are big gloves to fill because Simon was such an outstanding professional and contributed to the group even when not in the starting XI. Everything we know about Adrian tells us he has the personal qualities to go with his clear playing talent to ensure this area of the team is not weakened.
"We're all looking forward to working with him."