They won the semi-final 2-1 against Freiburg on Wednesday night and Ulreich was full of praise for the competitiveness Stuttgart showed on their way to the final.
"We've achieved our goal and it's a wonderful feeling to be in the final," he told Stuttgart's official website. "We gave our all in every cup game and remained highly concentrated throughout the competition.
"The feeling is very difficult to describe. I remember eagerly watching and celebrating the 1997 final as a fan – now I am there myself as a player.
"It's unbelievable! The fans gave us exceptional support, which I am very thankful for. [They were] super!"
Bayern Munich are the other finalists, having beaten Wolfsburg 6-1.