The Scot has been handed a six-year contract by the Old Trafford outfit, and will begin work as soon as the season is at an end.
"I'm looking forward to working with David and I believe I will have the same success I had with Sir Alex," Vidic said.
"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."
Moyes himself is honoured to have been given the chance to fill Ferguson's mighty shoes.
Although he will officially take up his post at the beginning of July, Moyes' work will start before then, with meetings planned with chief executive elect Ed Woodward to discuss their joint strategy going forward, having been given the strongest possible backing Ferguson.
"It is a great honour to be asked to be the next manager of Manchester United," said Moyes. "I am delighted Sir Alex saw fit to recommend me for the job. I have great respect for everything he has done."
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