The new chairman is Sir William Patey, the former UK Ambassador to Afghanistan, who has taken over with immediate effect.
It is understood that the board's forward plans for stadium redevelopment and potential negotiations with Swindon Borough Council has forced the change of leadership.
"Having met Sir William, I am confident he will bring great value to the Board of STFC, but, after much reflection, I have concluded that it would be inappropriate to accept the offer to remain on the Board and as such intend to terminate my engagement with the Club," commented Wray in a statement.
Wray, who took over as interim chairman in May 2011 after the resignation of Andrew Fitton, has overseen the appointment of Paolo Di Canio, enjoyed the club's promotion from League One and a Wembley final in the Johnstone's Paint Trophy during his tenure.
Di Canio has declined to speak to the media this week, but has released a statement admitting his disappointment at Wray's departure.
"It is important for me to have a team around me that I can trust. Jeremy Wray and Russell Backhouse, Phil Spencer and myself have worked tirelessly as a team to bring success to this club but now with Jeremy going and Russell potentially soon to depart, half of that team may soon be taken away, and, as much as I have loyalty to Swindon and its fans, I also have loyalty to Jeremy and Russell and these events have certainly changed the dynamics, but I am interested to learn the reasons behind this decision and what this means for me and the future of Swindon Town Football Club," he said.