"I'm looking forward to working with David and I believe I will have the same success I had with Sir Alex," Vidic told United's official website.
"David and Sir Alex share some similarities - they are very passionate, they are both winners and you can see the way they approach the games and how they run things."
It has been suggested Moyes will work his new charges hard in training, but that merely ties in with the regime that is about to reach its end.
"David Moyes did a great job with Everton," said Vidic.
"He is the man who gets his players to work hard and show discipline.
"He did that well with Everton because in the last few years they've been successful in getting into the top six."