Stella took over as McLaren's F1 team principal after Andres Seidl left late last year to join Sauber and manage its transition to becoming the Audi works team in 2026.
In 2023, Stella oversaw McLaren's considerable gains up the F1 pecking order, while also substantially changing the structure of its car design technical department.
In an exclusive interview with Motorsport.com, Brown said Stella had done an "outstanding job" since being moved up to team principal.
"He has been awesome," Brown continued. "That is obviously about what has happened on the track but the culture that he has created, the way he has empowered people, the way he has got the most out of people, the leadership he is providing – he is a fantastic leader."
When asked to provide examples of Stella's leadership benefitting McLaren, Brown replied: "Yes, a lot, one of his greatest strengths is he is a great communicator.
"And he is a great listener and he also canvasses a lot of opinion and he has a great ability to look at things through those people's lenses.
"Which is quite a talent. If I am an aero person, he hears what they are saying and digests it from their point of view. He listens, he debates, he empowers.
"I'll see him now on the pitwall, because he is in a slightly different role, but he will challenge [team strategy calls] and let them make decisions.
"He will only step in if there is a really wrong decision. But that is what you want to do as a leader.
"[His method involves saying] 'I am not sure I would do it that way but that is your job,' so there is a talent to letting people do things their way.
"He is a great communicator, leads by example."
Stella has also developed a reputation for detailed and patient media briefings in 2023, which Brown said reflected his position as a "people person".
"[But] don't be mistaken by his soft demeanour, he is tough," Brown added. "Tough, demanding, fair, leads by example.
"All the classic things you want in a great leader, that is Andrea.
"He is very articulative and it makes him a great communicator so he doesn't talk gibberish.
"Whether it is to the media [or anyone], he is clear and concise with the messages he delivers."
