Speedcafe.com revealed Seidl was set to leave the team for a new role at Sauber ahead of Audi's planned entry into Formula 1.
That has since been confirmed, with McLaren announcing Stella, formerly the Executive Director, Racing for the team, will step up.
“I feel privileged to take on the Team Principal role as the next stage of being part of the McLaren F1 Team,” said Stella.
“I am grateful to Zak and the Shareholders for their trust in me and to all my colleagues and those who have supported me throughout my F1 career.
“We are realistic about the amount of work ahead of us to move back up the grid, but I am excited and encouraged that I am in this journey together with a team full of talent, experience, racing spirit and dedication.
“I look forward to working closely with each of them, Lando and Oscar, to together achieving great success and enjoying the journey.”
“Andrea is a highly talented, experienced and respected member of our team with a strong track record of leadership and success in Formula 1.
“His move into this role is a great example of the strength in depth we have in our team, and I'm excited to be working more closely with him with a joint focus on moving up the grid and winning races.”
Brown also paid tribute to Seidl as the German prepares to leave the organisation.
“I've really enjoyed working with Andreas. He has provided great leadership for the team and has played a significant part in our F1 performance recovery plan and ongoing journey to return to the front of the grid,” he said.
“I thank him for the transparency throughout the process which gave us time to plan accordingly.”
Seidl joins Sauber Group as CEO, having headed its trackside operations earlier in his career.
It's expected there that he will play an integral role in Audi's introduction to Formula 1 after the German marque announced a “strategic partnership” with the Hinwil operation earlier this year.
“I joined McLaren in 2019 and have really enjoyed working with Zak and the team,” Seidl said of his time with McLaren.
“We have achieved some good results, and I will always have fond memories, with Monza being a personal and career highlight.
“The team is on a great trajectory, and I would like to thank everyone for their support, trust and commitment.
“Thanks to Zak and the shareholders for their understanding of my personal decision to move on to another challenge. I wish Andrea and the team all the best for the future.”