Rojo's future has been the centre of much speculation after United expressed an interest in the Argentina international following his exploits at the World Cup in Brazil last month.
United's attempts to sign Rojo hit a snag when Sporting and the Doyen agency, who own 75 per cent of the 24-year-old's rights, were embroiled in a public row over a potential transfer fee.
Rojo also missed training last week to force through a move to the Premier League, though he was later disciplined by the Portuguese club.
However, Rojo now finally appears set to link up with Louis van Gaal's side after speaking to Radio Continental in Argentina.
"It feels like a dream, to be a Manchester United player. Leaving Sporting wasn't easy," said Rojo, who missed Sporting's opening Primeira Liga fixture on Saturday.
"He [Juan Veron] told me about them when we played for Estudiantes."
Reports suggest Rojo will sign a four-year deal, with out-of-favour winger Nani to return to Sporting on loan.
