Fifa's decision not to reappoint ethics chiefs Hans-Joachim Eckert and Cornel Borbely means an effective end to the reform process, the pair say.
Swiss investigator Borbely and German judge Eckert were not named among those proposed for the next four-year term of the independent ethics committee.
Borbely and Eckert have combined to ban numerous football officials.
A statement from the pair said their impending departure "means the de facto end of Fifa's reform efforts".
World football's governing body launched a reform process following the arrests and indictment of several officials on bribery and corruption charges in 2015.
Borbely and Eckert suggested the decision not to reappoint them was "obviously politically motivated" and added: "It seems the Fifa hierarchy has valued its own and political interests higher than the long-term interests of Fifa."
Last year the committee investigated - and cleared - Fifa president Gianni Infantino of wrongdoing related to his expenses and sacking of whistleblowers.
Eckert's tenure has not been without criticism. In 2014 his report which cleared Russia and Qatar of corruption in the 2018 and 2022 World Cup bids was described as "erroneous and incomplete" by Michael Garcia, who had spent two years investigating the claims for Fifa.
BBC Sport understands Professor Miguel Maduro has also been fired as chairman of the Fifa Governance Committee - which in turn has led to committee member Professor Joseph Weiler resigning in protest.
Borbely and Eckert will be replaced by Colombian prosecutor Maria Claudia Rojas and Greek judge Vassilios Skouris, who was head of the European Court of Justice for 12 years until 2015.
The Fifa Council decisions were announced in Bahrain on Tuesday, two days before the 67th Fifa Congress.
Among the other announcements from the council was a decision not to end the bidding process for the 2026 World Cup by handing it to the joint North American bid from Canada, Mexico and the United States.
Rivals from other confederations only have until August to declare their intention to bid.
It was also confirmed that London will host of the Best Fifa Football Awards 2017 on 23 October, and that the ban on Iraq being able to play matches has been lifted.
BBC Radio 5 live sports news correspondent Richard Conway
Fifa was hoping to continue efforts to distance itself from a series of damaging corruption scandals in recent years at this week's annual congress in Bahrain - but its leading officials have decided that Borbely and Eckert are surplus to requirements.
The two ethics committee chiefs - who banned the former president Sepp Blatter and a host of other executives - wanted to stay on past their current mandate, but will now be replaced.
They also investigated but cleared Fifa's current president Gianni Infantino last year over the alleged misuse of private jets.
In a statement the pair said the decision to remove them "jeopardised" the future of the game.
They have now flown to Bahrain and will speak publicly on Wednesday in a dramatic move that threatens to undermine Fifa's well-laid plans to push the message here that the days of crisis are long behind them.