The 29-year-old has signed a four-year contract with Marcelo Bielsa's side, which secured promotion to the Premier League in 2019-2020.
The Spain international moves to Elland Road for a reported £26 million ($47.4 million)).
Rodrigo scored just seven goals in 34 appearances in all competitions last season, although his campaign was disrupted by knee problems.
Previously with Benfica, he was part of a treble-winning side in 2013-2014 and twice reached the UEFA Europa League final before joining Valencia in 2014.
He scored five goals in seven appearances in the Copa del Rey in 2018-2019, including the winner in the final against Barcelona, as Valencia lifted the trophy in its centenary year.
Leeds also announced the signing of Robin Koch from Bundesliga side SC Freiburg for an undisclosed fee on Sunday (AEST).
Koch, a 24-year-old centre back that has earned two international caps with Germany, has signed a four-year deal with Bielsa's side.
Hello Elland Road. 🤙🏼— Robin Koch (@RobinKoch25) August 29, 2020
I’m really proud to become part of such a historic club. I will do my best to take the next step with this team and bring a bright future to this city. Let’s do it! 💪🏼 @LUFC pic.twitter.com/yFSOCHPWH5