The 20-year-old Penarol full-back joined the Red Devils earlier this month to spend a few weeks training with the Premier League champions.
"I have trained with the first-team," Varela, who departed England late last week, told Tirando Paredes.
"I am very happy and I was received very well.
"It was a surprise to get the chance to test with Manchester United. I'm glad and happy, and grateful to Penarol who allowed me to travel.
"I was treated so well and Cicharito [Javier Hernandez] helped me a lot. The work outs were short but very demanding."