As outlined by Marca, the experienced shot-stopper has agreed a move to the Rome club after he became fed up of waiting for an offer from Los Che.
Officials at the Mestalla were reported to be hopeful of selling first-choice goalkeeper Jasper Cillessen this summer but are yet to negotiate on his departure, meaning they could not yet move for Reina, who subsequently grew impatient.
Dutch international Cillessen was said to be among the 12 first-team players at the club who were told they would be allowed to move clubs this summer amid a huge squad clearout at Los Che, where Dani Parejo, Francis Coquelin and Ferran Torres having already departed.
Indeed, a report Onda Cero earlier this month claimed Valencia had decided to make Reina their number one goalkeeper for next season but could only fund the move once Cillessen had been moved on.
Cillessen spent five seasons at Ajax between 2011 and 2016 before a move to Barcelona, but he played second fiddle to Marc-Andre Ter Stegen and moved to the Mestalla this summer, where he has made 30 appearances but his performance level has underwhelmed.
Reina, who will celebrate his 38th birthday this month, began his career at Barcelona before moving to Villarreal, but his most memorable stint was across a nine-year spell at Liverpool between 2005 and 2014.
He has since played for Bayern Munich and Napoli before his move to the Milanese giants in the summer of 2018.
The 37-year-old custodian has won a number of cup medals across his time with Liverpool and Napoli but played just five Serie A games for Milan before his January loan switch to the Premier League.