The 38-year-old Belgian was the surprise choice tasked with restoring Bayern Munich as the dominant force in German football, given he had just overseen Burnley being relegated from the Premier League last season.
Bayern come into the season on the back of a first trophyless campaign in 11 years.
Their thunder had been stolen by Bayer Leverkusen, who were unbeaten as they sealed a domestic league and cup double.
Kompany, who cut his teeth prior to Burnley coaching Anderlecht and guiding them to the 2022 Belgian Cup final, said he was satisfied with the preparations ahead of Sunday's match.
"No, definitely not nervous, but that was always the way with me," Kompany told reporters, adding "it's a big challenge."
"We've prepared ourselves well with the team and the coaching staff, now it's up to the players who will play tomorrow. I'm excited."
Kompany, who as a player won four Premier League titles with Manchester City and was capped 89 times, said Leverkusen, who opened their campaign with victory on Friday, will be formidable rivals again.
"Leverkusen were phenomenal last season," said Kompany.
"I think you'll need around 90 points for the title again, so we need the maximum performance from everyone."
Kompany said Michael Olise and Joao Palhinha, who arrived from Crystal Palace and Fulham respectively in the close season, were in line to make their debuts against Wolfsburg.
"There's a good chance they'll play a lot this season but I'll keep my secrets until tomorrow."
Wolfsburg have not beaten Bayern in 20 matches dating back to 2015.
