The Argentine defender is expected to complete the formalities of his "dream" move to Old Trafford in the near future after Sporting confirmed that Nani had moved the other way on what is understood to be a season-long loan deal.
Rojo believes that he will be able to adapt to the English game "easily" and also reiterated his apology for how he acted when trying to force the move.
"It's a dream to play at Manchester United and I am very proud of having the chance of working with Van Gaal. I spoke with Juan Sebastian Veron about Manchester United when we were at Estudiantes. I have always liked English football, and I should adapt to this new playing style easily," the 24-year-old told Continental.
"There was a misunderstanding, I never wanted to do something wrong at Sporting as I have always been very thankful to that team that gave me many chances for playing in Europe.
"If I made a mistake, I have already apologised because I didn't want to hurt the feelings of anyone at the club."
Rojo, who spent two years with Sporting, featured for his country at this summer's World Cup, playing all 120 minutes in the final against eventual winners Germany.