Cardiff Blues will also face a team who reached the last four in the previous campaign as they make the journey north to Scotstoun to take on Glasgow.
For the Ospreys, a trip to Italy is in store on the opening weekend as they meet Treviso.
Later in the season there are the regular local derby fixtures to look forward to over the festive period, whilst the final round of the regular season is scheduled for 9/10/11 May.
The play-offs follow a week later with the 2013/14 RaboDirect PRO12 season concluding with the final on the last weekend in May.
Tournament Director David Jordan commented: "It is 10 years since the competition changed to a home and away format and four years since the introduction of the end of season play-offs.
"During that time a regular season pattern has emerged and we have seen increases in both attendances and viewing figures so fans are obviously enjoying the rugby that is on offer in the RaboDirect PRO12.
"In the coming season, fans in the home unions have the added excitement of the victorious British & Irish Lions players returning to their clubs to look forward to as well.
"Since the inception of the competition five different teams have taken the title although interestingly, no champions have ever defended their crown. Leinster will have a challenge on their hands in the coming season."
RaboDirect PRO12 Season 2013/14
Round 1 - 6/7/8 September
Benetton Treviso v Ospreys
Connacht v Zebre
Glasgow Warriors v Cardiff Blues
Munster v Edinburgh Rugby
Newport Gwent Dragons v Ulster
Scarlets v Leinster
Round 2 - 13/14/15 September
Cardiff Blues v Connacht
Edinburgh Rugby v Newport Gwent Dragons
Leinster v Ospreys
Scarlets v Benetton Treviso
Ulster v Glasgow Warriors
Zebre v Munster