The 29-year-old has penned a four-year deal at Elland Road after Leeds reached an agreement with the Spanish club to pay £27 million (Dh132m).
"I'm really excited and very happy to join the club in this important season for all of us", he told the club's Twitter account.
In addition to Leeds United and Newcastle United, at least one other club from the Premier League are said to be in the race for the signature of the versatile German global.
Leeds were working on the deal for several weeks after it became clear that Valencia were prepared to sell the player during the ongoing transfer window.
"When Victor Orta called me, I knew I would have a chance at Leeds", Rodrigo concluded.
Four Chinese COVID-19 vaccines undergoing phase-3 clinical trials
Trials are separate from emergency-use authorization, but the two could potentially run in parallel in some countries. CanSino developed its COVID-19 vaccine in partnership with the Chinese Military Academy of Medical Science.
For the German sport media, almost every time a player leaves the Bundesliga for the Premier League... it's mainly about money. How people feel the football there is different from other countries.
Rodrigo scored 59 goals in 220 games for Valencia after he joined from Benfica in 2014, initially on loan, and bolsters Marcelo Bielsa's attacking options ahead of Leeds' first season back in the English top flight for 16 years.
Rodrigo has experience in English football, spending the 2010-11 season on loan at Bolton, making 21 appearances and scoring once.