Herrera was confirmed as a United player on Thursday, signing a four-year deal at Old Trafford with the option for a further year.
The move was completed after a buy-out clause in Herrera's contract was triggered, enabling him to leave Bilbao after three seasons.
And the 24-year-old midfielder is eagerly anticipating his United debut, having been heavily linked with the Premier League club 12 months ago.
Herrera revealed fellow Spaniards Juan Mata and David de Gea had provided him with positive feedback, and is looking forward to working under Louis van Gaal, who will take over as United manager after the FIFA World Cup.
"Louis van Gaal is one of the best managers in the world," Herrera told MUTV.
"I want to learn a lot of things and I can't wait to play for Manchester United."
Asked about the discussions he had with Mata and De Gea, Herrera added: "They told me this is the biggest club in the world."
In his three years at Bilbao, Herrera made 128 appearances and scored 11 goals.