Leeds announced on Saturday they had signed Spain international Rodrigo from Valencia for a club-record fee.
The forward has penned a four-year deal at Elland Road, reportedly costing the Premier League newcomers around £30 million ($40 million).
The 29-year-old said he was excited to join the club and was looking forward to working with Marcelo Bielsa, whom he described as one of the best coaches in football.
"It's a new step in my career and I want to help the team to achieve the goals of the season," he told the club's Twitter account.
"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."
Rodrigo, who can operate as a winger or striker, spent time at Celta Vigo and Real Madrid as a young player before moving to Benfica.
He joined Valencia in 2014, initially on loan, scoring 59 goals in 220 appearances.
He previously spent the 2010/11 season on loan at Bolton, then in the Premier League.
Rodrigo was born in Brazil but is a Spain international and has 22 caps and eight goals.
He scored 10 goals for club and country in 38 games last season, including the winner in Valencia's 1-0 Champions League win at Chelsea in September.
Later on Saturday Leeds announced that Freiburg defender Robin Koch had completed a move to Elland Road.
The 24-year-old Germany international, who has joined for an undisclosed fee, has signed a four-year deal.
Leeds finished 10 points clear at the top of the Championship last season, securing their return to the top flight for the first time since 2004.