The 20-year-old has signed for the Premier League champions from Uruguayan side Penarol for an undisclosed fee.
 
The Uruguayan spent two weeks at the club on trial in May and impressed the club's staff in training.
 
And he was elated to have signed for the Old Trafford outfit, given the global status and successful history of the club.
 
"I'm very pleased to be a part of this club, one of the best teams in the world," Varela told the club's official website.
 
"As everyone in the world knows, this is a huge club that has won everything and I really hope that continues."
 
Varela has made nine Under-20 appearances for his country and will feature at the FIFA Under-20 World Cup in Turkey later this month.
 
He does not believe the language barrier will be an issue at United, with a series of the club's players able to speak Spanish.
 
"I'm very lucky there are quite a few Spanish speakers here. It will certainly help me settle in," he said.
 
Varela made 23 appearances for Penarol in the Uruguyan top-flight last season.