The Owls brought in the relatively unknown coach at the end of last week to replace Carlos Carvalhal, who has since been taken on by top-flight side Swansea City.
Former Hertha Berlin, Stuttgart and Borussia Monchengladbach boss Luhukay arrives at Hillsborough with a tag of being a promotion expert of sorts, having twice taken clubs into the Bundesliga, and his next target is to revive Wednesday's own playoff hopes.
Speaking to reporters at his unveiling on Monday afternoon, the 54-year-old said: "I am very happy that Sheffield Wednesday have given me this chance as a trainer and a coach. It is a big highlight [of my career]. In the next weeks and months I will learn more about the whole club.
"I have worked for big clubs in Germany so can see how it is here. We will play good football, but, first it is important now to bring some stability. The team has not much confidence. In the last weeks and months it is not what everyone has wanted. The last two years was fantastic and the step to the Premier League was very close.
"The last two years I was often in London and watched a lot of games. I liked the football, it is great and the stadiums are big. The fans also have a lot of emotions and passion. That is why I like it very much to be a manager here. Step by step, I hope to give the team a lot of confidence and make the fans happy with what they see how we play football."
First up for Luhukay is a trip to face arch-rivals Sheffield United at Bramall Lane on Friday night, with Wednesday currently 13 point adrift of the top six.