The 29-year-old Spain striker has signed a four-year deal with Marcelo Bielsa’s newly-promoted side until the summer of 2024.
It was gathered that, Leeds agreed a £26m deal with valencia for the player on Tuesday, with a further £9m due in add ons.
The forward had a medical on Wednesday having agreed to a move after being persuaded by Leeds director of football Victor Orta and owner Andrea Radrizzani who visited Valencia on Monday to finalise the deal.
On his move to the Premier League, Rodrigo thanked the Leeds duo’s involvement and said: ‘I am really happy and I am very excited to join the club in this important season for all of us after coming back to the Premier League.
‘I want to thank all the fans on social media, the club, the president Andrea and Victor Orta for the effort.
‘As soon as I spoke with Victor, I knew I wanted this challenge with Leeds.
‘For me it is an important new step in my career and I want to help the team to achieve the goals of the season.’
Asked how big a factor Bielsa was in the move, Rodrigo added: ‘He is one of the best coaches in football at the moment.
‘He did important things in different clubs and of course I am really excited to learn from them and improve my football with hard work and team work and I hope we can do important things this season.’
Rodrigo has been an important player for Valencia in recent seasons, scoring 19 goals in the 2017-2018 campaign and 15 in 2018-2019, in which they won the Copa del Rey.
He only managed seven goals last season in an underwhelming campaign on a personal note as he missed the last few weeks of the campaign with a knee injury.