Garcia has the authority to order fresh probes into old cases, including claims about how FIFA executive committee members awarded the hosting rights for the 2018 and 2022 World Cups.
His appointment by that same ruling board as chairman of the prosecution unit in a revamped FIFA ethics court is seen as a crucial step in FIFA President Sepp Blatter's promised anti-corruption reforms.
"The decisions of this (ethics) committee will be accepted. There is no doubt," Blatter said at a news conference. "We have to follow what they are going to find out, whenever they are going to open cases. Now let them work."
FIFA also selected German judge Joachim Eckert to chair the judging chamber of its revamped, two-chamber ethics court.
Garcia and Eckert can start work now but their appointments will be formally ratified at the next FIFA Congress, scheduled for May 2013 in Mauritius.
Garcia brings a stellar reputation to football's embattled world governing body. He helped prosecute and convict terrorists who bombed the World Trade Center in 1993 while Assistant U.S. Attorney for the Southern District of New York, and has been suggested as a potential Director of the U.S. Federal Bureau of Investigation.
One of his first tasks will be to inspect a Swiss court document on a World Cup kickbacks scandal to evaluate the behaviour of Blatter and other senior FIFA officials in the affair. Former FIFA president Joao Havelange and former 2014 World Cup organizing head Ricardo Teixeira were finally identified last week for taking millions of dollars in payments from now-defunct marketing agency ISL.
"He (Garcia) will have not only to write, but the duty to have this case analyzed on ethic, moral matters and then to report back to the executive committee," Blatter said.
Garcia and Eckert are regarded as key independent figures from outside the so-called "football family" who can help restore FIFA's credibility after bribery and vote-buying scandals, plus the long-running ISL agency scandal which has tainted much of Blatter's 14-year presidency.
FIFA agreed that no statute of limitations on bribery and corruption claims should impede Garcia's work, Blatter said.
Blatter's ruling board agreed to modernize the ethics court to prosecute cases more effectively after a panel of anti-corruption experts advising FIFA said previous cases were "insufficiently investigated."
The 13-member panel, led by Swiss law professor Mark Pieth, wants Garcia to examine claims surrounding how Russia and Qatar were awarded 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 favours 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 fulfil a FIFA statute that neither they, nor their families, had a paid connection to football in the past four years.
They will receive the "normal compensation and payments" — widely reported as $500 daily expenses — for FIFA committee positions, Blatter said.
Garcia was linked to an expected vacancy to lead the FBI 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 the nomination of Garcia, who has also served on the board of international police agency Interpol.
FIFA declined to appoint war crimes prosecutor Luis Moreno-Ocampo of Argentina, who was widely reported to be the advisory panel's preferred choice.
Blatter was repeatedly asked if he would follow calls from some German football leaders to resign over the ISL scandal, and his suggestion last week of suspicions surrounding how Germany won the hosting rights for the 2006 World Cup.
"This can only be decided by the Congress," said the 76-year-old Swiss, referring to the 209 football nations who elect him. "If they don't want me any longer, I will say, 'OK, I have done my job and I will leave.'"