The former United States Attorney made the pledge in his first formal visit to FIFA headquarters at Zurich, after being appointed to help restore confidence in football's governing body after years of scandal involving bribery, vote-buying and ticket scams.
"If there is conduct in the past that warrants investigation, I will do it," Garcia told reporters in a conference call. "There are no limitations at all on what we will be looking at."
Days into his new task, Garcia has already been urged how to achieve it.
FIFA's anti-corruption advisers want him to probe how 2018 and 2022 World Cup hosting rights were awarded, and European politicians want him to examine FIFA President Sepp Blatter's election victory last year.
Garcia said his wide-ranging authority includes "whether that area is a particular World Cup or a particular individual."
He invited any "credible complaint of corruption" from whistleblowers, and plans to create a "pipeline" for people outside of FIFA's often secretive circles to suggest cases.
"I don't see any limitations on whistleblower or complaint intake ... or where complaints can come from," Garcia said. "I think it is my obligation and a responsibility under (FIFA's code of ethics) to do that."
Still, the lawyer who helped prosecute and convict terrorists in the 1993 World Trade Center bombing is already busy with two signature scandals that FIFA sent his way.
On Thursday, Garcia opened his first case and suspended Blatter's former election rival Mohamed bin Hammam for 90 days to investigate bribery allegations. They relate to the Qatari official's failed campaign last year, and earlier use of Asian Football Confederation accounts.
The second round of claims were levelled at bin Hammam last week, three days before he beat FIFA in a Court of Arbitration for Sport verdict which overturned his life ban from world football. CAS suggested bin Hammam was not innocent, and that FIFA could re-open the case.
"There are many facts and allegations in there," Garcia said of the court's decision.
Blatter has also passed Garcia a Swiss court document detailing aspects of a decade-old World Cup kickbacks scandal for his newly created investigations unit to assess.
Garcia was flanked Friday by German judge Joachim Eckert who will lead FIFA's new ethics court, and insisted they would be independent. FIFA has said both will be paid standard daily fees and expenses claimed by committee members while on football duty.
"We will not accept any influence exerted on us," said Eckert, who sat in judgment of a noted German bribery case involving industrial giant Siemens.
Garcia noted that past FIFA ethics prosecutions — conducted by some of the same officials who comprise his new team — often failed to get witnesses to co-operate. He plans to change that.
"It is incredibly important for this (ethics) code to contain penalties, sanctions, clear lines of obligations and duty to co-operate. That is a very powerful tool," he said.