The Penarol full-back spent time on trial at Old Trafford at the end of last season and David Moyes has given his approval for the deal to be completed.
Varela travelled over to London from Uruguay on Thursday and spoke to Futbol a lo Penarol radio before he left.
He said: "I will have a medical on Friday and on Saturday I join the Uruguay Under-20 national team.
"I will have to learn English, Rodolfo Catino [Penarol's club treasurer] taught me something, the structure is impressive."
Catino also spoke to Futbol a lo Penarol radio before travelling to England.
He added: "The deal has been agreed, we now have to discuss some points, there won't be any percentage regarding any future transfer.
"The deal can be as much as 2.8 million Euros. Guille will adapt quickly to Manchester."