The 23-year-old joined Liverpool from Fulham in 2019 and featured for the under-23 squad before heading to Blackburn Rovers on loan.
Elliott had a productive season in the Championship, scoring seven goals and providing 11 assists before returning to Anfield and forcing his way into the senior squad.
After falling down the pecking order, the Englishman joined Aston Villa on loan last season but barely featured, with the club looking to avoid triggering a permanent clause in the deal.
"We all wish Harvey the best of luck during his time with Valencia," the club said as part of a statement on their website.
He now heads to Valencia in a bid to start fresh after 149 appearances for the Reds, scoring 15 goals and playing his part in two Premier League title wins.
