Vidic picked up both awards after a season in which his formidable partnership at the back with Rio Ferdinand has played a major part in helping United retain their Barclays Premier League title.
The Serbia defender was delighted at the recognition for his achievements this season.
"It's a great night for me," Vidic told MUTV. "I'm really surprised but I'm enjoying it.
"In my career I have never really had individual awards.
"I am honoured especially when I see the players who I play every day with. It's amazing to get this award. I'm very happy. Thank you. I developed here as a player. Thank you to the players and the coaching staff.
"Since I came here three and a half years ago I have progressed every year and I'm proud of that. I enjoy it here. I like being with the players and I'm very happy here."
Team-mate Ryan Giggs has no doubt it was the right choice.
"So many players have had a good season," he said. But it has to be Nemanja for me.
"Consistently throughout the season he's been brilliant."