Goddard has played 128 games for the Bombers, after moving to the club ahead of the 2013 season after 205 games for St Kilda.
“Over the last few weeks I have had very open discussions with John about my playing future and I fully respect the club’s decision,” Goddard told essendonfc.com.au.
“I still feel as though I have something to give but fully respect the club has to make these hard decisions and it speaks to the depth of younger talent we have on our list.
“The club has been great to me over my six years and I feel I have been great for the club.
“I am at peace with the decision but still weighing up my options, given it is still very raw, I am taking some time to think about the future.
“I want to thank the Club for the opportunities it has given me and wish the Essendon Football Club every success in the future.”
Coach John Worsfold also spoke on Goddard’s time in red and black, and thanked the 33-year-old for his time at the club.
“Brendon and I have had open and honest conversations about his future at the club,” Worsfold told the club’s website.
“We informed him yesterday that the club would not extend his contact to 2019.
“As it was only yesterday that Brendon was given the news, he is still processing everything and coming to terms with the decision.
“He will speak when he is ready and has a clear idea on what his future looks like.
“Brendon has been an incredible leader of this club both on and off the field, and holds himself and his teammates to the highest standard.
“He has helped in developing a number of our younger athletes and helped support the Club and its growth over a challenging time.
“On behalf of the Essendon Football Club I would like to thank Brendon for everything he has given this Club and for the legacy he will leave behind.”