Olise was signed from Premier League club Crystal Palace for a reported fee of 60 million euros (£50.3m) in July but spent much of the pre-season playing for France at the Paris Olympics.
Despite his late start, Olise, who took home a silver medal after France were beaten by Spain in the Olympic final, has featured in all five of Bayern's matches across all competitions this season and scored three goals.
"Well, for me, it wasn't that bad that he went to the Olympic tournament, because he arrived in really good shape at Bayern Munich," Kompany told reporters.
"It's exactly what we were expecting. I think he's really playing a big role, which isn't easy when you've arrived in the Bundesliga and at a club like Bayern. He will take further steps.
"From my point of view, it's very positive, but I stay calm as well because I know it's important to continue the way he does in order to experience good times."
Bayern are first in the Bundesliga standings with nine points from three games, two clear of second-placed Borussia Dortmund and RB Leipzig in third.
Kompany's side visit eighth-placed Werder Bremen on Saturday in the most played fixture in Bundesliga history, with this the 115th meeting between the two sides.
"Bayern against Bremen is a traditional fixture," Kompany added.
"When I played in the Bundesliga, it was a top-of-the-table clash. Bremen have produced a lot of great players. It's a special game tomorrow and that's how we'll prepare it."
The Belgian manager added that he would make a late call on Manuel Neuer's selection after the veteran goalkeeper was substituted at halftime during Bayern's 9-2 Champions League win over Dinamo Zagreb on Tuesday.
"Neuer should join training today and we'll decide after that. We'll discuss it together," Kompany said.
"We didn't want to take any risks against Zagreb but it looks good. There's no other news."
On a lighter note, Kompany said he was looking forward to attending Oktoberfest, which begins on Saturday, adding: "We're looking forward to it but for the next 24 hours it's only about Werder.
"I come from Belgium where the beer is also top, like it is in Bavaria. We'll have a nice team outing on Sunday."
