Moyes already has a tough job replacing the great Alex Ferguson, who retired after nearly 27 trophy-laden years at Old Trafford, and the release of the 2013-14 fixture list hasn't given him any respite.
After opening its title defense at Swansea, United hosts Chelsea also under a new manager in Jose Mourinho the following weekend. Then United plays great rival Liverpool away before a trip to City on the weekend of Sept. 21.
Mourinho's first match in his second spell with Chelsea is at home to newly promoted Hull while Manuel Pellegrini's first taste of action as City's new manager comes at home to Newcastle.
The opening round of the season takes place on the weekend of Aug. 17-18.
Given all the managerial appointments among the big clubs, it is anticipated that this season's title race will be one of the most hotly contested in years.
If it goes down to the last day as it did two seasons ago United will be away at Southampton, City is at home to West Ham and Chelsea visits Cardiff, one of the other promoted teams.
Arsenal begins the season at home to Aston Villa, Liverpool hosts Stoke and the first game in charge for new Everton manager Roberto Martinez is at Norwich.