Argentina international Rojo signed for United from Sporting Lisbon last month in a deal worth £16 million, but has not yet featured for his new club due to delays in obtaining a visa.
However, he has now been granted the all clear to play, and is relishing the chance to line up alongside fellow new arrivals such as Radamel Falcao and Angel Di Maria.
"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," he 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."
Di Maria arrived from Real Madrid for a British record fee of £59.7m, making his debut at Burnley last time out, and Rojo is familiar with the attacker from their time with the Argentina national team.
"He's got a lot of quality," he proclaimed. "He is very sharp and very fast so he can help a lot attacking in the second line."
United - without a win from their opening three Premier League fixtures - recruited Monaco forward Falcao on loan on transfer deadline day.
"There are some good strikers in the squad," he added. "But Falcao is always in the penalty box; he is very sharp and capable to make the most of any chance.
"I will try to find my place as soon as possible and help in every way I can so we get important trophies."
United host QPR in the Premier League on Sunday.
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