The former West Ham United shot-stopper officially became a free agent on June 30, although the Reds were engaged in discussions with his entourage over a short-term extension.
However, after five seasons under the tutelage of Jurgen Klopp, Adrian has called time on his Liverpool career, and the Reds announced the departure of the 37-year-old on Sunday.
Posting a tribute to Adrian on X - formerly known as Twitter - Liverpool wrote: "Adrian departs Liverpool this summer having made a valuable contribution to the club's successes across his five years at Anfield.
"A popular figure among teammates and staff alike, Adrian leaves the Reds with the best wishes of everybody at the club. Thank you for everything, @AdriSanMiguel ❤️".
Having earned his Premier League stars during his six-year stint in a West Ham shirt, Adrian arrived at Anfield in the summer of 2019 on a free transfer, replacing the long-serving Simon Mignolet.
The former Real Betis youngster played a significant part in a trophy triumph in his first few weeks at the club, starting their 2019 UEFA Super Cup final success over Chelsea, saving Tammy Abraham's final spot kick.
Acting as Alisson Becker's backup in his debut campaign, Adrian managed 18 appearances in all tournaments in 2019-20 - including 11 in the Premier League and three in the Champions League - but the emergence of Caoimhin Kelleher relegated him to third choice.
Adrian played just eight more times for Liverpool over the course of four seasons, taking his total for the Reds to 26 appearances in all tournaments, during which time he kept seven clean sheets.
The Spaniard did not earn a single minute of competitive action last season, and his final game for Klopp's Liverpool came in the 2022 Community Shield, where he helped the Merseyside giants sink Manchester City 3-1.
What next for Adrian after Liverpool exit?
Now officially a free agent after following Joel Matip and Thiago Alcantara out of the door, Adrian is expected to finalise a return to boyhood club Real Betis in the not-so-distant future.
The 37-year-old confirmed his desire to go back to his homeland even before his Liverpool contract ran out, and he previously spent 15 years in the Betis ranks from 1998 until 2013.