The Dutchman will lead the Scottish Premier League giants in Seville next Wednesday against their Bundesliga rivals as the famous Glasgow club bid for only a second continental trophy.
Rangers were beaten by Zenit in the UEFA Cup final in Manchester 14 years ago
Their only previous taste of European glory came in the 1972 European Cup Winners' Cup final, which they won under Willie Waddell with a defeat of Dynamo Moscow in Barcelona.
Half a century on, Van Bronckhorst could repeat the feat with a triumph in Spain, and the Rangers boss is desperate to lift the trophy.
"It means a lot," he told a press conference. "There aren't many managers in the history of this club who played a European final.
"There's only one who actually won it. For the club, it would be fantastic to win a second prize in Europe."
Referring to the lack of European success for Scottish clubs, the Dutchman added: "It's not often you play finals, it's not often you play finals in Europe as a Scottish team.
"It's very rare that it happens. We're really honoured and proud that we are in the final in Seville, and can enjoy this occasion with many fans all around the world.
"We're representing this beautiful club, we're representing Scotland, so we have to make sure we give a good impression, and that's what we want to do."
Touching on his side's impressive exploits in beating RB Leipzig to reach the final, Van Bronckhorst says the memory will live him with a long time, while stressing the job is not yet done.
"The Leipzig game was one of the best nights I've experienced as a player and a manager," he added. "But it is very important that we keep going.
"The last two games we've played, against Dundee United and Ross County, we didn't relax because we need the same intensity, the same desire to play against Frankfurt.
"I don't want my players to slip up. Saturday [when Rangers play Hearts] is a bit different, because we're going to change some players, but I think we're ready for the final. That's all that matters now."