Dragons coach Paul Turner has criticised the play-off format
The Dragons will face Italian side Calvisano in the Heineken Cup play-off.
Calvisano lost to Benetton Treviso in the semi-final of the Italian Super 10, meaning that Treviso become the 23rd side to qualify for the Heineken Cup.
The 24th and final team will be decided on Friday when the Dragons travel to face Calvisano in a winner-takes-all clash (2000 BST).
The winners will enter the 2009/10 Heineken Cup, the losers going into the second-tier Challenge Cup competition.
Dragons coach Paul Turner has criticised the season structure and the play-off system his side now has to endure.
"It's not ideal, I suppose it's not a great way to run a business," said Turner.
"[There's] too many games in one patch, which we've had during the season, and then not enough in another.
"We've got a good enough squad to go out to Italy and win, there's no question about that.
Turner had previously said: "What the mindset will be, well that's down to me, I've got to be quite positive about this and whether it's Calvisano or Treviso it's places we've been to before and won.
"We've obviously got boys out of contract two days after that game and looking for pastures new, so it's not ideal, but I suppose we've got to get on with it."
The Dragons finished as the bottom Welsh region in the Magners League but above the bottom Irish side, meaning that they entered the play-off.