The 50-year-old dual British and Cayman Islands citizen has relinquished his passports to the FBI and must remain within a 20-mile (32-kilometer) radius of the US federal court in Brooklyn.
He is the first former official from soccer's governing body to appear in a New York court in connection with the sweeping international scandal that has rocked the sporting world.
He was flown to New York from Switzerland earlier this week, the only one of seven FIFA officials arrested in Zurich not to contest extradition.
In all, 14 defendants stand accused of soliciting and receiving more than USD 150 million in bribes and kickbacks across 24 years.
More From This Section
US Attorney General Loretta Lynch unveiled the 47-count indictment in May, charging soccer officials and marketing executives with racketeering, wire fraud and money laundering conspiracies.
Besides serving as FIFA vice president, Webb was president of the Cayman Islands football association as well as CONCACAF, which oversees the sport in North and Central America and the Caribbean.