The Spaniard stepped down from his position on Thursday morning after just under two years at the helm.
It represented a huge surprise to Town supporters, with some national reports suggesting that he is the subject of interest from a rival club.
Corberan's long-term colleague Jorge Alarcón has also left the club.
Danny Schofield will take charge of the team, assisted by Narcis Pèlach and existing staff.
Corberan, who took Town to the Championship play-off final last season, when they were edged out by Nottingham Forest, spoke fondly of his time at the club in a farewell statement on social media.
But after much thought, he deemed it to be the right time to leave.
Corberan, 39, who moved to Huddersfield from his role as under-23 head coach at Leeds United, said: "The dav has come that I will verv likely remember for the rest of my life.
"Today my time as head coach at Huddersfield Town has come to an end and I say goodbye to all of you with an open
"It has been a difficult decision, but one I gave a lot of thought to and have made based on my great affection for this club.
"As a coach, my approach to my work is based exclusively on the strongest commitment to and utmost alignment with the policy of the club I'm serving because that is the only way to ensure the dedication required to manage a football team.
"Leading this club over the past two seasons has been a pleasure and made me feel extremely
"However, I have the utmost respect towards everyone at this club and its supporters and that is why I feel the need for us to end our relationship.
"There are times in life when the most honest thing to do is to step aside on amicable terms in the best interests of both parties.
"I would like to thank Phil Hodgkinson, who appointed me during his time as chairman; Leigh Bromby, who offered me the fantastic opportunity to coach in the Championship and believed in me, which is something I will never forget; and Dean Hoyle, the club's current chairman, for his massive contribution and for injecting great energy and enthusiasm when the club needed it most.
"I also want to mention all of the members of the incredible staff I worked with and all of the club employees who were such a great help during my time.
"Of course, a special mention goes to the players I worked with, who showed themselves to be exceptional human beings.
"You all know just how special you are to me. You have made me a better coach than I was when I joined the club two years ago.
"And, of course, thank you to the fans for all of your support and kindness. I thank you all: those who were convinced from day one and those who the team managed to convince as the games wore on. I want to give you my heartfelt thanks. Huddersfield Town have a family in the stands and that is the greatest of treasures."