Rodrigo moves to Elland Road on a four-year contract to become Marcelo Bielsa’s seventh summer signing.
Leeds United are back in the Premier League after a 16-year hiatus and will take on champions Liverpool in the opening weekend of the season.
Rodrigo has previously played in the Premier League with Bolton Wanderers, where he spent the 2010/2011 season on loan from Benfica, and scored one goal in 16 appearances.
The 29-year-old Spain international is the latest high profile player to leave Valencia in the close season after the likes of Ferran Torres, Dani Parejo and Francis Coquelin all departed the Mestalla Stadium.
Rodrigo made 34 appearances in all competitions for Valencia last season and scored seven goals as Los Che finished ninth in La Liga and reached the Champions League round of 16 stage, where they lost out to Atalanta.
“I’m really excited and very happy to join the club in this important season for all of us,” Rodrigo said.
“It’s a new step in my career and I want to help the team to achieve the goals of the season. Leeds have been working for two weeks on this deal with Valencia, we knew Valencia have some problems now as we didn’t achieve the Champions League.
“Since the first time Victor Orta (director of football) talked to me I knew I wanted this new challenge with Leeds. I will be working with one of the best coaches (Marcelo Bielsa) in football, he has done important things in different clubs and I’m excited to learn.”
Leeds United’s previous record buy was the £18m they paid West Ham United for Rio Ferdinand in 2000.
Rodrigo made 220 appearances in six years for Valencia and scored 59 goals.
He has been capped 22 times for the Spain national team and scored eight goals.
