Varela impressed in a two-week trial at Carrington in May and will now vie with Chilean striker Angelo Henriquez (signed in September 2012 but loaned to Wigan Athletic shortly afterwards) to become the 11th South American to make a first-team appearance for the Reds.
The defender, who will represent Uruguay at the Under-20 World Cup in Turkey later this month, is looking forward to starting life at Old Trafford next season.
?I?m very pleased to be a part of this club, one of the best teams in the world,? he said. ?As everyone in the world knows, this is a huge club that has won everything and I really hope that continues." The Uruguayan told ManUtd.com.
Varela should settle quickly into the United dressing room given the global make-up of the Reds squad.
?I?m very lucky there are quite a few Spanish-speakers here,? he said. ?It will certainly help me settle in.?
What sort of a player is he?
He's a quick, aggressive right-back who has a real willingness to defend. In that respect, he's not a typical South American defender in terms of wanting to be a forward player and joining in attacks as a winger.
What are his strengths?
As well as his desire to defend, he is a composed individual and nothing seems to faze him. Overall, he's a no-nonsense defender who reads the game well and uses his intelligence.
What can he improve on?
His pace allows him to get forward to join attacks quickly but his attacking work is probably the area he will aim to develop most at United.
When did he catch United's eye?
Playing in the Under-20 World Cup qualifiers for Uruguay in Argentina. He was playing with team-mates he was not familiar with and yet still displayed a good understanding of the game. Despite a tough schedule in very hot temperatures, his stamina and strength shone through while other players wilted.
How did his trial period at Carrington pan out?
He was with the first team for 10 days or so at the end of the season. It was a unique trial in many ways because he trained with the first team during his entire spell. Obviously, if you're not up to that level, you get exposed quickly in the first-team group but his performances are believed to have impressed Sir Alex and the rest of the players.
Which former United player is he most like?
Although he is not as big physically yet, there is a little bit of Gabriel Heinze's style about him in terms of his approach to the game. If he does as well as the Argentinian, everybody will be delighted.
Will he be able to settle in a new country?
There is already a group of young Spanish-speakers at Old Trafford ? the likes of David De Gea, Javier Hernandez and Angelo Henriquez ? who can help him with the language and adapting to life in Manchester. Hernandez was a big help on the training pitch during his trial period, passing on the coaching instructions.