The Scot's first game at Old Trafford is a tricky test against Jose Mourinho's Chelsea a week later, before a trip to Liverpool awaits on August 31.
The first Manchester derby of the season is pencilled in for the Etihad Stadium on September 21, while Moyes comes up against his former club Everton (H) on December 3.
United tackle Hull at the KC Stadium on Boxing Day and entertain Tottenham on New Year's Day.
The return with fierce rivals City is scheduled for March 1 and Moyes returns to Goodison Park on April 19.
The season finishes with a home game against Sunderland on May 3 and trip to Southampton a week later.