The move brings to an end a torrid few months for the 23-year-old, who was left out of Liverpool's first two Premier League squads of the season despite featuring regularly for Andoni Iraola during pre-season.
Explaining the decision before Elliott's departure, the Liverpool head coach had been candid about the competition for places: "With Harvey... I can only choose 20. Harvey is trying and improving every week but I still prefer other options, about the balance on the bench."
Elliott arrived at Manises airport on Monday to complete the final steps of a move that will see him join on loan until the end of June 2027, with no option to buy included in the agreement.
Liverpool and Valencia have also reached an understanding to split the midfielder's wages for the duration of the deal, according to Spanish reports, helping unblock a transfer that had looked financially complex for the LaLiga club. He is still subject to passing a medical and signing his contract before the move is finalised.
It is Elliott's second successive season away from Anfield, after a difficult loan at Aston Villa in which he made only a single Premier League start.
"To be honest, everything happened pretty quickly, but I was ready to get the call," Elliott said of his move to Mestalla.
"I just had to make sure I was ready to come here and play, and I am. Now I'm here and I'm really looking forward to the weekend."
Asked about his personal goals, Elliott set his sights high.
"I hope I can help take Valencia into European competition," he said. "Valencia is an incredible club and I want to do everything I can for them. I think, especially with the squad we have, we're capable of achieving it. It's going to be a tough season, but I have a lot of confidence."
Head coach Carlos Corberán is understood to have personally called Elliott to outline the role he could play in the project, a factor in accelerating the deal in its final stages.
"It's an incredible club and I'm very grateful for the opportunity," Elliott said. "I'm going to give my best here and I know the history this club has. This all takes a lot of work, and for my part, I'm going to give everything for Valencia."
A product of Fulham's academy before joining Liverpool in 2019, Elliott has operated as an attacking midfielder, a central midfielder and a right winger throughout his career, and made his Premier League debut aged just 16.
"I can play in any position. I'm just happy to play football, but I think as an attacking midfielder, as a No. 10, is where I'm most effective," he said.