"The UK Border Agency has agreed to grant #mufc defender MarcosRojo5 a visa and he will therefore be available to face QPR on 14 September," an official United statement said on social media.
The 24-year-old signed for the club from Sporting Lisbon for £16m last month, but has been unavailable to play until the permit was granted.
Rojo qualified automatically by virtue of having played in more than 75 per cent of Argentina’s competitive internationals over the last two years, including the World Cup final against Germany in July.
He is likely to feature in United's next clash against the R's at Old Trafford, with Louis van Gaal's side still searching for their first Premier League win of the season.
The defender has kept himself fit while waiting to get the go-ahead to play for his new club and featured for the South Americans in their 4-2 friendly win against Germany in Dusseldorf on Wednesday night.