Herrera was a target for Van Gaal's predecessor David Moyes 12 months ago, but he remained at Athletic Bilbao when the transfer window closed.
United have moved much quicker for Herrera this summer and, earlier this week, he became van Gaal’s first signing since the Dutchman was named Moyes' successor.
Van Gaal is currently with the Netherlands squad at the World Cup and Herrera cannot wait to work with the former Ajax and Barcelona coach.
"Louis van Gaal is one of the best managers in the world and, for me, I am lucky to be working with him," Herrera told MUTV.
"I want to learn a lot of things and I cannot wait to play with van Gaal, my new team-mates and for Manchester United.
"I'm really excited to go on pre-season to America and play against Roma and Inter Milan."
Herrera has outlined the qualities he will bring to United and he is looking forward to the prospect of testing himself in the Premier League.
He added: "I am a midfielder and one of the best qualities I have is that I always want to be involved. I want the ball and want to help my team-mates.
"I know the Premier League and really like it. I think I will grow up in the Premier League. It is one of the best leagues in the world."
The 24-year-old will link up with David de Gea and Juan Mata at Old Trafford, and Herrera has spoken to his fellow Spaniards about playing for United.
"I know they are very happy," he said. "I was talking to them and they told me this is the biggest club in the world and that we have a very good squad.
"They can help me settle at Manchester United. We are very good friends and I'm sure they will help me adapt at the club."