Garcia was elected to head the investigative branch of FIFA's newly-reformed ethics committee while German judge Hans-Joachim Eckert was appointed to head the tribunal which will judge cases and hand out sanctions.
"He [Garcia] will have not only the right but the duty to have this case analysed on ethics and moral grounds and then to report back to the executive committee," FIFA president Sepp Blatter told reporters.
"The chairmen of both chambers are totally independent, this had been requested by FIFA's Congress," added Blatter.
The election of Garcia was a surprise as it had been widely reported that the task would be given to top international prosecutor Luis Moreno-Ocampo, best known for pursuing war criminals.
A Swiss prosecutor said in a legal document released last week that former FIFA president Joao Havelange and former executive committee member Ricardo Teixeira took multi-million bribes on World Cup deals in the 1990s.
The bribes were paid by FIFA's former marketing partner ISL which collapsed in 2001.
Blatter was general secretary under Havelange and attention has centered on whether he knew about the payments.
Havelange is FIFA's honorary president while Teixeira quit as head of the Brazilian Football Confederation (CBF) earlier this year.
