Tosic joined the Red Devils along with Adem Ljajic from Partizan Belgrade in a deal that could end up costing United £17million.
“At the beginning it was a dream to play somewhere like United but now it is a reality, one I am very happy with,” he told Uefa’s official website.
“I want to become a top player at United and not waste the opportunity of being a member of the greatest football family.
“It is great feeling, but now I must think about working hard.
“The presence of Nemanja Vidic will be a great help as I know him from the national team. I am full of confidence, will learn quickly and hope United can count on me very soon.”