The governing body, which oversees British horseracing, will begin the process of selecting a new CEO in the next few weeks.
Rust said: “I’ve spent much of the past year reflecting on my situation after my personal bereavement at the end of 2018.
“This is a fantastic job leading a team of passionate, hard-working people who want racing to have a prosperous and sustainable future as a clean, fair sport that looks after its horses and its people.
“With the committed support of our new Chair, Annamarie Phelps, the BHA has put itself, and helped put our sport, in a place where we can be optimistic about our future. The foundations for success are in place.”
Annamarie Phelps, the BHA’s Chair, said: “We’re all going to miss Nick’s passions and drive. It is typical of his deep commitment to British racing that he’s given us plenty of time to find a new leader, avoiding a vacuum and ensuring a seamless transition.
“He’s been a great help to me personally over the last few months as I’ve got to know the sport and the industry.”
