Whistleblower David Phelan claimed patients were removed from lists at Kettering General Hospital because national targets were being missed.
The hospital admitted it used data filtering to get a "true picture of the size of its waiting list" but the practice had stopped in December 2015.
Graham Foster and David Sissling have announced their resignations.
The hospital said former chief executive Mr Sissling had to take prolonged sick leave from his position in September 2016 after suffering a brain haemorrhage.
While he is much recovered he has decided not to return to the chief executive role.
Former chairman Mr Foster has announced he would also now like to resign to enable a new chairman and a new chief executive to be recruited together.
He said: "I feel the appointment of a new chief executive would be best achieved with a chairman who is committed to the trust for at least three years given the scale of challenges faced."
Mr Foster joined the trust as chairman on 1 September 2013, with Mr Sissling arriving in April 2014.
Current interim chief executive, Fiona Wise, will continue in her role until December.
At the end of last month a BBC investigation found thousands of Kettering General Hospital patients had waited a year or more for operations.
The hospital admitted there had been "anomalies" and claimed its data management had been "well intended, if misguided".
It denied it was trying to seek any "financial advantage" from its actions.
The chairman and chief executive of a hospital accused of altering waiting list numbers have resigned.