United complete 20m euro Rojo signing
In this picture taken on June 25, 2014, Argentina's defender Marcos Rojo celebrates his goal during a Group F football match against Nigeria at the Beira-Rio Stadium in Porto Alegre during the 2014 FIFA World Cup - by Pedro Ugarte
Rojo signed a five-year contract after impressing during the World Cup where he helped Argentina to reach the final.
Winger Nani has gone in the other direction, rejoining Sporting on a season-long loan, seven years after he left the Portuguese club.
"It is such an honour to say that I now play for Manchester United. The Premier League is the most exciting league in the world and to have the chance to play in it for the world's biggest club is a dream for me," said Rojo.
"I am young and am very keen to continue to learn the game, so playing for such an experienced technical coach as Louis van Gaal is a fantastic opportunity for me. I have joined United to work hard with my team-mates to win trophies and I know that the manager shares that ambition."
Rojo spent the past two seasons at Sporting having joined from Spartak Moscow in July 2012.
"Marcos is a very gifted defender. He has played at the highest level in world football and can play either as a central defender or left-back," said Van Gaal.
"He has ability, physical strength and a willingness to learn that means he has a very bright future ahead of him. He had a very strong World Cup and has been playing in Europe for a couple of years now. He is a very good addition to the team."