The Eagles' board decided on Monday night the time was right to move on from Simpson, with the decision made public on Tuesday morning.
Simpson fronted the media alongside chief executive Don Pyke and chairman Paul Fitzpatrick on Tuesday afternoon to explain the "mutual" decision.
The 2018 premiership coach will still decide whether to coach against the Lions on Sunday.
If Simpson does decide to do it, it would mark a memorable farewell for someone who is still adored by Eagles fans despite the disastrous run of on-field results over the past few years.
"I haven't made that call quite yet," Simpson said.
"Obviously a decision's been made (to change coach) and it's mutual.
"I feel like the time is right. I've been reasonably stoic over the last few years about the direction of the club.
"It's a slow burn, it's going to take a bit of time.
"Someone else will come in now, a bit like when I took over from Woosha (John Worsfold) at the end of 2013.
"Someone comes in with energy and gets to grow with the group. I think it's the right call."
The West Coast Eagles and senior coach Adam Simpson have mutually agreed that his 11-year tenure at the club will come to an end.— West Coast Eagles (@WestCoastEagles) https://t.co/DbgH6ksb9LJuly 9, 2024
Pyke, a former coach at Adelaide, ruled himself out of being either West Coast's interim coach or the next full-time senior coach.
Instead, Pyke will play a key role in his chief executive position in choosing the next senior coach.
Eagles premiership star Cox, who is an assistant at Sydney, is considered among the early frontrunners.
Former West Coast forward Hansen, who is currently an assistant at Carlton, could also be a contender.
West Coast assistant Jarrad Schofield and Fremantle assistant Jaymie Graham are other highly respected figures who could be sounded out.
"Clearly today our situation changes, so we're in the market for a new coach, and that process will start now," Pyke said.
"We'll put a list of people to approach and start talking to about leading the club going forward."
Pyke said they will also finalise an interim coach, with that person to be needed as early as this weekend if Simpson decides to step away immediately.
Eagles players gave Simpson a rousing reception at the end of Tuesday's press conference.
Simpson, who was contracted until the end of 2025, was almost axed at the end of last year and he knew the heat was on him again.
"We respect the last three years have been tough on the club and particularly Adam as coach," Pyke said.
"The discussions I've had with Adam and the board - it was time. It was time for a change, it was time for a refresh of our program.
"And to Adam's great credit, he always puts the club first, and he respected that was going to be the position and he had no more to give.
"We've requested Adam consider coaching the side for one final time this weekend. We'd love Adam to coach one more time."
The early parting of ways is set to cost West Coast around a million dollars.
Simpson has been at the helm of West Coast since the end of 2013, guiding the club to the 2015 grand final and the 2018 flag.
But the Eagles' fall from grace over the past few years resulted in the spotlight being shone squarely on him.
West Coast have won just eight of their past 57 games, with the heat intensifying even more following lacklustre losses to Hawthorn and Melbourne over the past fortnight.
Reports of a text message leak last week in which three players expressed their desire for Simpson to be moved on added further pressure on the club.
