And the No.8, alongside fellow Lions such as Sean O'Brien, Cian Healy and the retiring Brian O'Driscoll, will now bid for glory on home turf at the RDS on May 31.
The semi-final win did not come easily however as Leinster found themselves nine points down at the hour-mark, only to battle back and emerge with a 13-9 victory.
And Heaslip believes Leinster were a team transformed in the second half after cutting out the ill-discipline that helped Ulster gain the initial foothold.
"We gave ourselves a mountain to climb I suppose, I think it was 9-0 at one stage and that's never easy, especially against a team like Ulster," he said.
"I think we gave them a lot of easy access points, I felt that our defence was quite solid in the first half and we gave away silly penalties that allowed them to get that lead.
"In the second half I thought we held on to the ball quite well, produced a lot of quick ball and held on to the ball.
"Our front row did an amazing job in the scrum and gave me an unbelievable platform at the back to keep it in and keep driving. We crept out the win in the end.
"Now we're in a final we want to win, we haven't looked at it yet because we were focused on this game."