With Andreas Seidl leaving to join the Sauber Group as chief executive, Andrea Stella moves from his role as racing director to take over as team principal at Woking.
Seidl - who had been contracted until 2025 - will start his new job with Sauber in January, filling the vacancy left by Ferrari-bound Fred Vasseur.
Brown revealed once it was clear Seidl was set to move to a fresh challenge, Stella - who had 15 years of experience at Ferrari - was the first person he wanted to call.
"Here we are with Andrea and as our team principle, which myself, our drivers and our team is extremely excited about," Brown said.
"Andrea obviously has a wealth of experience, not only with McLaren, but a rich history with Ferrari, so was someone that we knew who knew the team inside out.
"He is a very hands-on person in the racing team, which was of high interest to me and the shareholders, to have someone leading the team that gets their hands dirty so to speak, so we are very excited."
Brown added: "We have done a lot of promotion from within and have got a really solid racing team.
"The response I have had from the racing team about Andrea's employment has been predictably very well received.
"As we try and build a team to get back to competing for world championships, it has to be a team effort.
"This feels like we won't miss a beat versus introducing someone from the outside because it takes quite a ways to get up to speed.
"If we didn't have Andrea, that maybe would have been an alternative to look at, but it was very clear to all of us very quickly that Andrea was who we wanted to have on the team."
Stella joined McLaren in 2015, also having worked as both head of race operations and the Woking-based F1 team's performance director.
"There's clearly elements of continuation," the Italian said. "I think we worked very well with Andreas, we established some very important directions and we do want to consolidate them.
"At the same time, the vast study and the complexity of Formula One leaves the business always open for opportunities.
"This is what I am thinking about intensively together with my leaders at McLaren, so that we can find the further opportunities to go even faster towards achieving our mission."
Stella added: "I will be close to the core objectives of the team, which ultimately is to build a quick car and race this car effectively while on track."