Darren Grayson has stepped down from the East Sussex Healthcare NHS Trust, which runs the Conquest Hospital in St Leonards and Eastbourne District General Hospital (EDGH).
In March the Care Quality Commission said A&E waiting times were "excessive" and targets were being missed.
Campaigners have called for the resignation of the board of the trust.
Mr Grayson said: "Having been chief executive in East Sussex for five years, and having led the organisation through some significant change to improve the quality of our services for patients, I believe the time is now right to hand the baton to the next leader to continue this journey of improvement."
In its latest report in March, the CQC said it had particular concerns over outpatient records and surgical practices at the EDGH.
Liz Walke, chairwoman of the Save the DGH Campaign, said: "It's a start. Let's be clear, that it isn't just Darren Grayson. We think the board should go and, unless you have a clean sweep, no significant change will happen.
"We hope there isn't going to be a massive payout. We are hoping that he has just fallen on his sword."
Former Liberal Democrat MP for Eastbourne Stephen Lloyd said: "It's about time.
"Frankly, I called for it a good 18 months ago. He still appeared to be hanging on for grim death to the post. I just thought it was absolutely outrageous."
The chief executive of two Sussex hospitals, which the health watchdog said were inadequate, has resigned.