The two sides were pitted together in the biggest tie of the round which presents the German with a romantic reunion with the side he left last summer.
“I am really happy with the draw,” Klopp told liverpoolfc.com.
“Yesterday I said why should I wish [to get] the strongest team in the tournament, but obviously if you want to win the Europa League, and when you are in the quarter-final, then you have to beat the strongest teams. It is better to play against them in two games than in only one game.
“I am really happy to introduce my new team to Dortmund. I am really happy to show the boys this wonderful stadium and a great city. It’s a story only football can write.”
The other ties see Braga of Portugal play Shakhtar Donetsk and Villarreal meet Sparta Prague while there will be an all-Spanish clash between Athletic Bilbao and holders Sevilla, chasing a third straight success.
Klopp believes his players now feel comfortable with his style of play and that is being reflected in results.
Progress into the quarter-finals of the Europa League at the expense of arch-rivals Manchester United after a 1-1 draw at Old Trafford - and a 3-1 aggregate win - means they have not lost in 90 minutes since early February.
Included in that sequence is the Capital One Cup final penalty shoot-out defeat to Manchester City and a last-minute FA Cup loss at West Ham but also takes in wins over City and United.
Klopp believes momentum has been generated by a greater understanding of his tactics and not merely an improvement in confidence.
“The problem with confidence is it is like a little flower: if you step on it, it is away in a second - it is much more difficult to let it grow then to let it die,” said the German.
“It is not only about confidence, it is more about feeling more and more trust in our way of play. I don’t know in this moment how much we ran yesterday but especially in the first game it was really intensive but only 112 kilometres (were covered by the players).
“When I started here it was 119, 120 and we didn’t win. The only reason for counter- pressing is to win the ball back as quick as possible otherwise you have to make too many kilometres.
"That makes no sense. This is a real development and that is more important than confidence because the players have quality and we always have an offensive line-up so it is important we feel better in this style.”
Progression against United was seen as a significant moment in Liverpool’s season, with a return to Premier League action next at Southampton tomorrow.
However, a relaxed Klopp was in a laidback mood, arriving for his pre-match press conference in jeans and T-shirt with The Beatles logo on it.
The Reds boss has to endure a couple of puns based on Fab Four-related songs - with references to enjoying a Hard Day’s Night at Old Trafford and having a Ticket to Ride to the Europa League final - before he felt the need to put a halt to the teasing.
“I am not too good on all the Beatles songs,” he said. “You can carry on making jokes about it but I don’t understand!”
It is not the first time the German has referenced the city’s famous musicians since arriving on Merseyside in October.
Ahead of the visit of Manchester United in January he described former Red Devils boss Alex Ferguson as “the John Lennon of football” - which was probably not appreciated as much by Liverpool fans as his T-shirt tribute.
Europa League quarter-final draw:
Borussia Dortmund v Liverpool
Athletic Bilbao v Sevilla
Villarreal v Sparta Prague
Braga v Shakhtar
Ties to be played on Thursday April 7 and Thursday April 14.