The OBR assesses the health of the UK's economy. It is independent of the government but works closely with the Treasury.
The OBR's early publication effectively confirmed a number of new Budget measures - including a three-year freeze on income tax and National Insurance thresholds - before the chancellor announced them, throwing her Budget into chaos.
On Monday the report into the mishap concluded it had "inflicted heavy damage on the OBR's reputation" and had been "seriously disruptive" to the chancellor, but added that it was inadvertent.
The "ultimate responsibility" for the circumstances which meant people could access the report early lay with the OBR's leadership, the report added.
In a letter sent to both the chancellor and the chair of the Treasury Select Committee, Dame Meg Hillier, Mr Hughes said he believed the OBR could "quickly regain and restore the confidence and esteem" it had earned by implementing the report's recommendations.
"But I also need to play my part in enabling the organisation that I have loved leading for the past five years to quickly move on from this regrettable incident," he continued.
"I have, therefore, decided it is in the best interest of the OBR for me to resign as its Chair and take full responsibility to the shortcomings identified in the report."
Mr Hughes had been due to face questions from the Treasury Select Committee on Tuesday about the Budget and the OBR's economic forecasts, but Dame Meg confirmed that he would no longer attend.
In response to his resignation, Chancellor Rachel Reeves said: "I want to thank Richard Hughes for his public service and for leading the Office for Budget Responsibility over the past five years and for his many years of public service."