Edinburgh stunned Connacht 26-25 at the Sportsground on Saturday after Ulster's 20-13 away victory over Glasgow on Friday night. The finalists will meet at a Scottish venue still to be determined.
Connacht centre Darren Yapp had the misfortune to be the first player in Celtic rugby history to score a hat-trick of tries yet still be on the losing side, as the talents of Edinburgh play-maker Brendan Laney kept the Scottish side in front at crucial times.
Ulster called on their Australian contingent to win at Hughenden, with centre Ryan Constable scoring the try and fly-half Adam Larkin kicking the points.
Ulster chief executive Michael Reid said: We are delighted to have reached the final of the Celtic Cup. We played Edinburgh at Meadowbank earlier this season in the Celtic League but they will be much stronger with the return of their World Cup contingent and in Cup Final rugby anything can happen.
With another Celtic League match and two Heineken Cup pool games to be played before the final we will just be raring to go come the 20th of December.
The Celtic Cup final is Ulster's first chance of silverware since the European Cup win in 1999 and so has a massive significance to both players and fans - it's an honour to contest this inaugural final.
Reid said the recent improvement in the Ulster side was heartening. We've made real strides this season in bringing through a number of young players, and with the six players that travelled to Australia as part of the Irish World Cup squad now well and truly back in the fold and with several players due to return from injury, we can hopefully look forward to having almost a full complement of players to select from.
Our support in Glasgow last Friday night was phenomenal - over 500 made the trip to Hughenden and when you add to that our legion of exiled students, it was like having an extra man on the pitch.
Edinburgh chief executive Jim McKenzie said it was an exciting time for the club and their players.We felt we were probably 10 points better than Connacht on the day, but that didn't stop it from being an exciting finish, he said. They were peppering the posts with dropped goal attempts at the end, but we were able to hang on.
Even though we had lost there earlier in the season, we travelled feeling pretty confident of reaching the final and now we have a very exciting prospect in front of us.
It will be the first time that a professional Scottish team has played in an international, cross-border Cup final.
"There's a big prize to be won and everyone connected with the club is hoping that the whole of Scottish rugby will get behind us.
We should have a full-strength squad available, including eight returning World Cup players, and it's going to be a great occasion.
McKenzie said an early-season mauling at the hands of the Irish side just added to the excitement. We came off very much second-best against Ulster early in the season, but we aren't daunted by the prospect of facing them again. Instead, there's a great air of excitement at the club.