The Scotsman, who replaced Sir Alex Ferguson this summer, will take his side to Wembley this Sunday for an FA Community Shield clash against the Latics before beginning the new season with a trip to Swansea City.
"David has succeeded Sir Alex on merit," The Independent quotes Coyle as saying. "For years I have been saying he could manage any top club in world football. There is no doubting what he has done.
"He was a natural successor to Sir Alex and it is great to see a home-grown manager evolving to that level. I have no doubts he will have huge success at Manchester United."
Moyes's first competitive clash at Old Trafford will be against Chelsea on August 26.