The 13-member panel, led by Swiss law professor Mark Pieth, wants Garcia to examine claims surrounding how Russia and Qatar came to get World Cup hosting rights in a December 2010 poll of FIFA’s executive committee.
Several senior FIFA officials were reported to have received payments or sought unethical favors from bidders, and Blatter has acknowledged that some breached bidding rules by joining a pact to back Qatar and the failed Spain-Portugal bid.
Garcia and Eckert had to fulfill a FIFA statute that neither they, nor their families, had a paid connection to football in the past four years.
Garcia was linked to an expected vacancy to lead the U.S. Federal Bureau of Investigation last year, before President Barack Obama extended the term of 10-year incumbent Robert Mueller.
During the administration of President George W. Bush, Garcia headed the 20,000-employee Immigrations and Customs Enforcement agency in the Department of Homeland Security.
Eckert, who was a presiding state court judge in Munich, is a specialist in high-profile bribery cases including one which exposed billion-dollar payments made by German telecommunications firm Siemens.
Pieth’s group suggested four candidates for each of the positions decided on Tuesday, including Eckert. FIFA looked elsewhere for Garcia’s nomination.
FIFA declined to appoint war crimes prosecutor Luis Moreno-Ocampo of Argentina who was widely reported to be the advisory panel’s preferred choice.