Sporting Lisbon have agreed to sell Argentina's World Cup defender Marcos Rojo to Manchester United while Nani will move the other way as he joins the Portuguese side on loan.

Sporting said in a statement to Portugal's Market Securities Commission that the Premier League side would pay £16million for the 24-year-old and the Portuguese side would not pay anything for a one-year loan for Nani.

If Rojo is sold on in the future for more than £18.5million, Sporting will receive 20% of that fee, the club added.

Sporting have also claimed United will give them £7.2million to help build a new indoor arena in exchange for securing Rojo's services.

In a statement on their website, Manchester United said: "We are delighted to announce we have reached an agreement with Sporting Lisbon to sign defender Marcos Rojo, subject to a medical and agreeing personal terms."

Rojo told an Argentine radio station: "It's a dream to play at Manchester United and I am very proud of having the chance of working with Louis Van Gaal.

"I spoke with Juan Sebastian Veron about Manchester United when we were at Estudiantes. I have always liked English football, and I should adapt to this new playing style easily."

Rojo - who can play at centre-back or left-back - had an excellent World Cup as part of an Argentina defence that conceded only four goals in seven games as they finished runners-up to Germany.

Nani, 27, will return to the club he left seven years ago to join United.

He had a disappointing last season at Old Trafford and also under-performed for Portugal at the World Cup, despite scoring against the United States.