Van Bommel took over shortly after Belgium's quarter-final exit at the 2026 FIFA World Cup, with Rudi Garcia leaving his role after the Belgian Football Association decided not to extend his contract.
Courtois said Van Bommel's appointment was expected and believes his achievements in club football, combined with his playing career at the highest level, will earn the respect of Belgium's squad.
"It wasn't really a surprise because his name had been circulating for quite a while," Courtois said.
"I think he proved at Antwerp that he's a top coach. A lot of the players speak very positively about him, so I'm looking forward to getting to know him."
The experienced goalkeeper believes Van Bommel's time as an elite player gives him an important advantage.
"The most important thing is that Van Bommel himself played at the highest level and knows what it's like to play matches like these.
"That top-level experience is definitely a positive and it naturally earns a lot of respect from the players."
Courtois has not yet decided whether he will continue his international career, despite previously saying he wanted to play on after the World Cup.
The 34-year-old explained that his future depends on discussions with the new coach, as he hopes to sit out Belgium's upcoming UEFA Nations League campaign before making a final decision.
"After the World Cup, I definitely still want to continue, but it will depend on the conversation I have with him," Courtois said.
"I'd like to have some rest during the Nations League and we'll have to try to reach an agreement on that.
"After that, I'll decide whether I want to continue or not."
Courtois also looked back on Belgium's dramatic World Cup exit to eventual champions Spain.
The goalkeeper was forced off with an injury during the quarter-final in Los Angeles, before replacement Senne Lammens made a costly mistake that helped Spain secure a 2-1 victory.
Courtois believes he was still capable of finishing the match.
"I just felt that I couldn't take goal kicks anymore," he said.
"A defender could have taken them instead. During open play, I could still have made sideways passes.
"But the coach said: 'We agreed that only players who are 100 per cent fit will play.' Fine, no problem."
Despite criticism aimed at former coach Garcia following Belgium's World Cup campaign, Courtois insisted there was never any conflict between them.
"Of course, I was disappointed because it was against Spain and we were in a good rhythm. But the team is more important than I am.
"The decision was made and there was never any bad blood. I never wanted to speak badly about him."
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