The 53-year-old took charge of the club in April 2013, having previously worked at Reading.
Leeds owner Massimo Cellino stated on the club's official website: "Brian is a great manager and a great guy. He has been unfortunate to work in such difficult circumstances. I did not fully understand the mess he had to work in, and the broken promises he had to deal with, until I have got involved trying to turn Leeds around.
"He has been a gentleman to deal with in our discussions and has been very understanding of my wish to implement a new structure. His main concern and priority at all times has been the welfare and protection of Leeds United. I wish him well for the future where I am sure he will continue to have more success and thank him for his efforts in being a stabilising and unifying figure behind the scenes in very difficult circumstances.
"His honest efforts to guide us to the safety of mid-table when faced with many difficulties is appreciated by us all. He will always be a friend of Leeds United."
"It has been my great privilege to manage this great club and I have enjoyed the challenge immensely," McDermott told the club's website.
"However it is clear that Massimo wishes to implement a new structure and feels he will work more successfully for Leeds with a coach rather than a manager. I respect that Massimo must be fully supported in putting together his vision for the club so he can bring us the success we all want.
"It is my belief that when truly United we are stronger. Massimo wants to bring a new energy to the club so that we can return to where we belong as a healthy football club."
McDermott guided Leeds to a 15th-place finish in the Championship last season.