Garcia said he had lost confidence in the independence of the ethics committee's adjudicatory chamber following a 42-page statement issued by Eckert, based on Garcia's still-secret report, in November.
In comments which are likely to deal another blow to the credibility of FIFA's ability to police itself, Garcia also said that sport's world authority lacked leadership.
UEFA president Michel Platini, a member of FIFA's executive committee, said Garcia's resignation was a step backwards.
"FIFA's ethics committee was created to increase the transparency of the organisation, that's what we wanted, but in the end it has just caused more confusion for FIFA," the Frenchman said in a statement.
FIFA president Sepp Blatter added: "I am surprised by Mr Garcia's decision. The work of the Ethics Committee will nonetheless continue and will be a central part of the discussions at the ExCo meeting in the next two days."
Former U.S. prosecutor Garcia's report examined allegations of corruption in the awards of the 2018 and 2022 World Cup tournaments to Russia and Qatar respectively.
Garcia, who formerly served as chief federal prosecutor in Manhattan, had appealed against Eckert's statement, saying it contained misrepresentations, but that appeal was ruled inadmissible by FIFA on Tuesday.
FINAL WORD
"It now appears that, at least for the foreseeable future, the Eckert Decision will stand as the final word on the 2018/2022 FIFA World Cup bidding process," Garcia said in a statement, adding that a further appeal to the Court of Arbitration for Sport would be impractical.
"No independent governance committee, investigator, or arbitration panel can change the culture of an organization.
"And while the November 13, 2014, Eckert Decision made me lose confidence in the independence of the Adjudicatory Chamber, it is the lack of leadership on these issues within FIFA that leads me to conclude that my role in this process is at an end."
German judge Eckert's statement recommended that there was not enough evidence to justify reopening the bidding process for the 2018 and 2022 World Cup tournaments.
"The issues raised by Mr. Eckert's selection and omission of material from the Report, and his additional comments, went far beyond the initial transparency concerns," added Garcia.
"As my public statement at the time explained, the Eckert Decision contained "numerous materially incomplete and erroneous representations of facts and conclusions"."
Garcia said in Wednesday's statement that his report "identified serious and wide-ranging issues with the bidding and selection process."
Garcia also revealed that FIFA's executive committee reported him for publicly asking them to authorise publication of his report.
"The Chairman of the Disciplinary Committee, Claudio Sulser, ultimately rejected the Executive Committee's referral," he said.
MAKING PROGRESS
Garcia, who was appointed in 2012 and spent 18 months probing the 2018/2022 bidding process, said he felt that initially the ethics committee was making progress.
"For the first two years after my July 2012 appointment as independent Chairman of the FIFA Ethics Committee's Investigatory Chamber, I felt that the Ethics Committee was making real progress in advancing ethics enforcement at FIFA," he said. "In recent months, that changed."
FIFA's Executive Committee is meeting in Marrakech, which is hosting the Club World Club, this week.
The Exco is due to debate a proposal from Germany's Theo Zwanziger to allow the publication of Garcia's report in full.
FIFA and Qatar World Cup organisers have been fending off allegations of corruption ever since the Gulf state was awarded the 2022 tournament.
Qatar, which has repeatedly denied the allegations, has also been criticised over its treatment of migrant workers in the construction industry.
