Sullivan emphasised that none of the allegations concerned his involvement in football. He highlighted his long association with the game and his commitment to West Ham throughout more than three decades in the sport.
Explaining his decision, he said: "At what is already a challenging and important time for the club, I refuse to allow personal matters concerning me to become an unnecessary distraction or a source of instability.
"Therefore, after very careful consideration and with a heavy heart, I have decided to resign as Joint-Chair and Director of West Ham United FC with immediate effect.
"This has been an incredibly painful decision to make, but it is one made out of love, respect, and responsibility toward a football club and a fan base that deserve absolute unity and focus moving forward."