The 44-year-old German-born former USA international was yesterday appointed on a 12-month rolling contract as Chris Powell’s successor.
Wagner, a former member of Klopp’s coaching staff at Borussia Dortmund, will have a watching brief during tomorrow’s lunchtime derby with Leeds United before taking over on Monday.
This means Lillis, in his fourth spell as stand-in boss, will oversee the Leeds clash while admitting to being excited by the appointment of Town’s first foreign coach.
Supporters have been left equally buoyed by the arrival of such a close ally of Klopp, who had been expected to take Wagner to Liverpool as part of his backroom staff.
Asked if Town fans could expect a similar style of football under the club’s new head coach as that played by Dortmund under Klopp, Academy chief Lillis said: “We don’t know, but we will back him whatever.
“I like Mr Klopp. He is a good man. I like the way he patrols his dugout and he is enthusiastic, a bit like myself.
“It will be good if he (Wagner) can (bring Dortmund’s approach to Huddersfield). But he will be his own man.
“You have to be that when you go into a new club. You have to get across to the players what you are about, as the dressing room is massively important.”
Wagner spent four years in charge of Dortmund’s reserve team, which plays in the German equivalent of League One.
During his time at the helm of what is effectively an Under-23 outfit, he helped bring through a host of young players including Erik Durm, Jonas Hofmann, Marian Sarr and Marvin Ducksch.
This ability to develop youth potential was a big factor in Huddersfield opting to bring in Wagner, who as the club’s first head coach will work closely with head of football operations, Stuart Webber.
Chairman Dean Hoyle said: “His approach is a winning one. He is a head coach that sets his teams up on the front foot to win matches.
“He is up for the challenge of making Huddersfield Town a success on the pitch in the Championship.
“He also understands and believes in the club’s plan of producing and developing its own players. That was a major part of his job in charge of Borussia Dortmund II. He knows what it takes to prepare young footballers for the rigours of senior football.
“Perhaps most importantly, he has trust in young players, which is attractive to us.”
Wagner’s reign will not start officially until Monday, but he will be in the main stand tomorrow for the derby against Leeds.
It is a game Lillis, who has overseen 11 matches in three previous spells as temporary boss of Town, is desperate to win.
He added: “The main thing for me is Saturday at 12.30pm. That is my focus, the focus of the players and the staff. Same for the fans.
“I know from living in the town just what it means. I also know what it is like to play in a derby, I scored in one (against Leeds) in the Eighties – a 1-0 win at home.
“In my career, I also played in derby games in Nottingham, Manchester, Birmingham. Great games to play in and ones you have to end with no regrets.
“To go and manage a team in a derby is massive. Saturday, though, is not about me. It is about the players, the fans and the club.”
Once the Leeds clash is out of the way, Lillis will revert to being head of the Academy. It is a role that will mean working closely with Wagner, who will be assisted at the John Smith’s Stadium by Christoph Buhler.
Lillis added: “I hope he likes curries, as I will be taking him out for a curry and maybe a beer.
“It is a must to have a close relationship with the new head coach because of the direction the club wants to go in.
“It is good for me that he has a track record for helping young players. When I came into the club three and a half years ago, I didn’t like pretty, pretty Academy football, with a little trick here and a little trick there.
“Instead, we play proper football in our Academy. In the German League, they do the same.
“Their academies play in the equivalent of our League Two – men’s football.
“We have to produce Championship players and, ultimately, Premier League players. We are not in League One or Two any more.”