Van Gaal welcomed £150m worth of talent to Old Trafford during the summer in a spending spree that included the likes of Rojo, Daley Blind and Angel di Maria, with Radamel Falcao also signing on loan.
"It is a huge step forward in my career and my life and I am very happy to play for one of the best clubs in the world at the moment," Rojo told Perform.
"There are some great players [here]. We obviously need to give time so the new manager can build his team.
"But with the great names we have in our squad and the intelligence of the manager I am sure many achievements will come along."
United host Queens Park Rangers on Sunday hoping to get their first victory of the season having failed to win any of their previous three games - one defeat and two draws.
It is not yet known if Falcao, who had to obtain a working visa, is eligible for selection.