The club initially had an application for a permit knocked back for the 19-year-old on the grounds Anderson does not have enough international caps but United on Friday won an appeal against that decision.
It means the attacking midfielder, who signed from Portuguese side FC Porto last month, will be part of the United squad for next season.
The club said in a statement: "Manchester United is pleased to confirm that the club has been successful in its application for a work permit for Anderson."
United's representatives attended a Home Office panel of experts on Thursday where they argued that due to his exceptional talent he should be granted a work permit and that only his youth had prevented him from obtaining the requisite number of international caps.
Indeed, Anderson only made his full international debut for Brazil in the early hours of Thursday morning in the Copa America match against Mexico.
Anderson said earlier this week: "To join Manchester United at 19 is incredible.
"Everything will be different in England - I know that - but I am certain I will adjust quickly to life in England.
"I am proud - and my family is also. For me, everything is new, it's a dream come true."
Vi bruger cookies for at kunne give dig den bedste oplevelse. Ved at bruge vores side accepterer du brugen af cookies. Du kan læse mere i vores persondatapolitik.