Rugby Calvisano reached the play-off as the best placed non qualified Italian team in the Super 10 Championship having lost to Viadana on points difference over the two legs of the semi-finals.
Super 10 finalists Viadana and Benetton Treviso claiming automatic Italian Heineken spots.
The Dragons have qualified for the 24th place play-off for next season's Heineken Cup as the highest placed team in the Magners League who has not automatically qualified for next season's European tournament.
Dragons will meet Calvisano at Rodney Parade on Friday, 18 May with the game kicking off at 7.45pm in front of the Sky Sports cameras. The match will be refereed by English official Rob Debney with Martin Fox and Ashley Reay his touch judges.