The 29-year-old has signed a four-year deal with Marco Bielsa's side who return to the Premier League after a 16-year absence.
"For me this is a new step in my career and I want to help the team achieve the goals of the season," Rodrigo said in a statement.
"Of course Marcelo Bielsa is one of the best coaches in football at this moment, he has done important things at different clubs and I'm excited to learn from him, improve my football with hard work and teamwork and I hope we can do important things this season."
Rodrigo spent six seasons with Valencia and made 220 appearances across all competitions, scoring 59 goals.
He had a brief stint in the Premier League during the 2010-11 season when he joined Bolton Wanderers on loan and made 17 appearances.
He made 120 appearances for the Portuguese side across all competitions and scored 45 goals during his three seasons there.
Rodrigo won the under-21 European Championship with Spain in 2013 and has 22 senior caps, scoring eight goals.