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."
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.”
Fans will be able to watch an exclusive interview with Guillermo Varela on ManUtd.com at 16:00 BST.