The 20-year-old full-back arrives from Penarol and has signed a five-year contract with the Premier League champions
The 20-year-old has signed a five-year contract with the Premier League champions after completing a medical.
Varela, who had a two-week trial with United in May, will play for Uruguay at the Under-21 World Cup in Turkey which begins on June 21.
“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.
“I’m very lucky there are quite a few Spanish-speakers here. It will certainly help me settle in.”