The Woking-based squad announced on Tuesday that it was appointing Andrea Stella as its new team principal to replace Seidl.
As part of a team boss merry-go-round, Seidl has been lured away to join Sauber as its new CEO, in the wake of the Swiss-based outfit losing Fred Vasseur to Ferrari.
It comes as Sauber prepares to become Audi's works team from 2026.
Seidl's departure from McLaren was a bit of a shock, with him under a long-term contract that ran until the end of 2025.
However, McLaren CEO Zak Brown has explained that, with Seidl having informed him that he would join Audi when his current deal ended, an agreement was reached with Sauber to let him switch early as it hunted for a replacement for Vasseur.
Speaking to selected media from the McLaren factory on Tuesday, Brown said: "[Andreas] informed me during the season that he was going to go elsewhere when his contract was up at the end of 2025.
"[It was] probably pretty clear where that destination would be, which was quite understandable, given his background.
"At that time, we intended to continue for the foreseeable future, because the relationship is very, very healthy. And his work discipline is very strong.
"What we were going to do at that point was, at the end of the season, let the world know that that change would come in at the end of the '25 season.
"And, after we intended to go public, the first person I was going to call to see if they would lead McLaren's F1 team is the gentleman sitting next to me, Andrea [Stella] - but not at that point, being sure whether that would be something that he would consider.
"When it became clear that Fred was going to go to Ferrari, [Sauber owner] Finn Rausing, who is someone that I've known for a decade, and get along with very well, gave me a call to see if there was a discussion to be had to potentially release Andreas early.
"My reaction was, if Andrea would be happy to join as team principal, then I'd be very happy to make that change now, which I think puts everyone in their permanent homes for the foreseeable future."
Brown said after Rausing's approach, he eventually convinced Stella to step up to the role immediately – which opened the door for Seidl's exit.
"After some good conversations, Andrea kindly accepted the role, which then put us in a very comfortable position to move forward," he said.
"Because Andrea was always our number one choice to lead the team moving forward, that all came together quite rapidly."
Brown declined to elaborate on when exactly Seidl told him he would be leaving at the end of his contract.
He was clear, however, that there was no interest from McLaren's side in playing contractual games with Seidl and putting him on gardening leave.
"We have a great relationship," he said. "I know a lot of teams play the gardening leave card. But I think, as we've demonstrated at McLaren, there are ways to dissolve relationships, whether that's with racing drivers, or employees, where you can do things on very workable terms for everyone."
