The 59-year-old Dutchman has been targeted by the club’s fans along with members of the board following a poor start to the season.
Ahead of Monday’s home game against Arsenal, Everton lie 16th on the Premier League table, without a win in their last eight games.
Brands had been at the club since the summer of 2018.
A club statement said: "The owner and directors would like to thank Marcel for the service he has given to the club over the past three-and-a half-years and wish him well for his future.
"A strategic review of the football structure will now take place which will inform the best model for the club to proceed with in the long term.
"In the meantime, the owner and board of directors will continue to provide our manager, Rafa Benitez, with their full support."
Brands added: "On Friday, following a personal conversation with the chairman and my fellow board members, we agreed that I would step down from my post as director of football and as a member of the Everton football club board.
"This decision has taken some time and some consideration and was one of the most difficult I have faced in my career.
"The board and I agreed that there is a clear difference in the vision and direction for this beautiful club and, with that in mind, the decision was taken.
"I want to thank everyone in the club who I have worked closely with over the last three-and-a-half years. There are a lot of talented people at Everton with huge passion and commitment to move the club forward, both on and off the pitch.
"I want to wish all of the squad every success, and I am convinced that there is enough quality to improve the current situation quickly.
"It has been an honour for me to work at this fantastic club and I wish everyone associated with Everton the very best for the future."
