Varela joined United from Penarol in June 2013, but initially struggled to make an impact at Old Trafford due to the stiff competitions for places.
He has become a first-team regular in recent weeks as Louis van Gaal has been forced to turn to youth amid a growing injury crisis at Old Trafford, and Mata is impressed with Varela's rise to prominence.
"I'm very pleased and I'm very happy for him because he is doing very good on the right side," Mata told MUTV.
"He's going forward, he's defending very well, he's being aggressive and he's performing like he has been playing for 10 years before.
"That is very difficult when you are young and in a stadium such as Old Trafford. He's a very competitive guy, he's very good for the team and the dressing room so we are very happy for him."
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Marcos Rojo, meanwhile, is equally happy with Varela's presence at United and has hailed his relationship with the right-back.
"I am very happy for him as he has been playing well," Rojo added.
"It's not too long since we met and we've become mates. He's also my chauffeur. He takes me to all the matches as we live close by, so he's been doing all the driving which is fine by me.
"In the last few months we have spent a lot of time together and we have become really good mates. He's a really good guy, a great person and a big player for United."
Varela, 22, has made eight appearances for United since making his official debut in the scoreless draw with West Ham back in December.