The Uruguay Under-20s international spent the end of last season on trial at Old Trafford and impressed coaches enough to make a permanent move to the Premier League side.
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Speaking before the announcement of the transfer, Varela told Futbol a lo Penarol radio: "I will have a medical on Friday and on Saturday I join the Uruguay Under-20s national team.
"I will have to learn English. Rodolfo Catino [Penarol's club treasurer] taught me something. The structure is impressive."
Catino, who travelled with Varela in order to complete the deal on behalf of the club, believes that the promising youngster can settle into life in a new country.
"The deal has been agreed," he added. "There won't be any percentage regarding any future transfer.
"The deal can be as much as €2.8 million (£2.4m). Guille will adapt quickly to Manchester."