New manager David Moyes, who was appointed after Alex Ferguson retired in May, takes his team to south Wales on August 17 and will take charge for his first home game the following week.
United's opponents for Moyes' debut at Old Trafford will be Europa League-winners Chelsea, with Jose Mourinho reinstalled as manager and hungry for fresh success.
Both fixtures last year ended in away wins.
Moyes, meanwhile, returns to Everton, where he was manager for 11 years, on April 19.
Chelsea begin their campaign at home against newly promoted Hull City, while Manuel Pellegrini will get his first taste of English top-flight football when Manchester City welcome Newcastle United to Eastlands.
Arsene Wenger's Arsenal take on Aston Villa at the Emirates in their opener, while Tottenham Hotspur travel to promoted Crystal Palace.
Last year's third promoted team from the Championship, Cardiff City, travel to West Ham.
Moyes and Pellegrini will taste the highly charged atmosphere of the Manchester derby for the first time on September 21, when City host United, with the return fixture at Old Trafford on March 1, 2014.
The corresponding fixtures last season were won by the away side.
Northwest England rivals Liverpool play Manchester United at Anfield on August 31, with the return fixture on March 15.
The two dates for the north London derby between Arsenal and Spurs are August 31 and March 15, with high-scoring expected after the last six games yielding 31 goals.
The Merseyside derbies between Roberto Martinez's Everton and Liverpool take place on November 23 and January 28.
Cardiff City and Swansea City play in the Premier League's first Welsh derby in Cardiff on November 2, with both sides meeting again at the Liberty Stadium on February 8.
The first Tyneside derby sees Newcastle United travel to Sunderland on October 26, with the Magpies' Alan Pardew seeking revenge after the Black Cats took four points off them last season.
The season runs through until May 11 when Manchester United, Chelsea and Arsenal -- who are all expected to be in the running for the title -- playing away.
United are at Southampton, Chelsea at Cardiff and Arsenal play Norwich City. Manchester City play West Ham United at home.
Last season's relegated clubs QPR, Wigan Athletic and Reading begin their fight for a return to the top flight with opening matches against Sheffield Wednesday, Barnsley and Ipswich in the Championship.
England's Football Association, meanwhile, announced that the final of the FA Cup would take place on May 17 -- a week after the end of the Premier League season.
Since 2010, the traditional finale to the season has had to share the spotlight with a weekend of league fixtures and last year's winners, Wigan, still had a relegation battle to fight.
"We're well aware that fans and media have been calling for the the FA Cup final to have a day to itself and we're delighted that this is going to happen for 2014," said FA general secretary Alex Horne.