After crashing out of the Europa League in the group stages two years ago, Dortmund's return to the Champions League ended in equally embarrassing circumstances with only one win and a draw from six group matches last term.
The side who have not been beaten in their last 31 Bundesliga appearances have so far failed to show Europe why German opponents have such fear of them, but the time has come for that to change, according to Klopp.
"We now feel like we totally belong here, and we are ready for action," he said.
"The way Bayern Munich have got on in the Champions League, and the way we have played against Bayern and how stable we were there, that gives us good pointers."
However, Dortmund could hardly have been given a tougher draw in their bid to crack Europe at the third attempt.
After tomorrow night's opponents Ajax, the Westphalians have to take on the might of Real Madrid and Manchester City.
"It is a group in which heroes will be born," announced Dortmund's general manager Hans-Joachim Watzke after the draw was made.
Klopp added: "This is a fantastic story, this group. It is one which gives us anticipation, goose bumps and jittery nerves."
The time has come for those nerves to be transformed into positive energy, something Klopp expects from the 65,000 fans inside the Westfalenstadion.
"It is going to be a fantastic game in an extraordinary atmosphere," he said. "Ajax are a great side, they play football and are technically strong."
Ajax exited the Champions League at the group stage last year and then bowed out of the Europa League after losing narrowly to Manchester United in the round of 32.
The Amsterdammers' boss Frank de Boer is hoping his players can eliminate the mistakes which blighted their campaign in 2011/12 and learn from the experience of playing the likes of Real Madrid.
"It is going to be a tough challenge, but of course we have a chance, if we dare to play football," he said.
"We played well against Real Madrid last year, but after carelessly losing possession, the ball was in the back of our net.
"Hopefully we have learned from that because not all of us have experience in the Champions League."