Even as top soccer officials were still being arrested as part of a sprawling corruption investigation in 2015, lawyers for the sport’s global governing body and U.S. prosecutors began to embrace an intriguing premise:

The soccer organization, FIFA, and its affiliates were not only the hosts of the scheme, the thinking went, they were also its victims.

For prosecutors, the notion distinguished between the hijackers and the hijacked: It held individuals accountable for their crimes but spared the organizations and the sport that they had defrauded. For FIFA and its new leaders and lawyers, the framing had a bigger benefit: It protected against prosecution, and it offered the organization a chance to reclaim the tens of millions of dollars siphoned away by corrupt officials.

Tuesday brought the payoff: Six years after a wide-ranging criminal indictment laid bare decades of corruption in global soccer on a stunning scale, and five years after those in power started pursuing a piece of the millions that American authorities were rounding up, the U.S. government approved the payment of more than $200 million to FIFA and its two member confederations most implicated in the scandal.

The repayment will begin with an initial payment of $32.3 million in forfeited funds, the Justice Department said, but prosecutors have approved a plan in which the soccer organizations could receive as much as $201 million.

In a statement, FIFA’s president, Gianni Infantino, thanked the American authorities for their “fast and effective approach in bringing these matters to a conclusion, and also for their trust in general,” adding that soccer now considered itself “well past” its corrupt history.

“We will make sure that these funds are used properly and bring tangible benefits for people who really need it,” Infantino said.

The repayments will be directed to FIFA as well as to CONCACAF, the organization overseeing soccer in North and Central America and the Caribbean, and CONMEBOL, which governs the sport in South America. The previous leaders of those organizations, as well as those of national soccer federations across the Americas, had been implicated in the scandal in colorful detail. More than 50 people and companies were charged in the case, and dozens have pleaded guilty. Along the way, at least two defendants have died.

The Justice Department’s decision to return millions of dollars suggested a measure of restored faith in FIFA’s management, even as the money — something the organization first requested years ago — came with strings attached: It must be walled off in a foundation and directed toward developing soccer around the world, according to Tuesday’s announcement. A significant portion of the money will be directed to projects in the Americas, FIFA said, “given that they suffered significantly as a result of the criminal activities.”

Any spending from the new account, the World Football Remission Fund, will be subject to oversight and independent audit measures, American authorities said.

The money will be held in the U.S. bank system instead of in Switzerland, where FIFA has its headquarters, according to the terms of the agreement, which were described by two people familiar with the arrangement who requested anonymity because they were not authorized to discuss the details publicly.

Parameters for spending money recovered from the government have figured into other corruption cases, like the United Nations oil for food case, in which the Justice Department specifically designated restitution money for a development fund in Iraq.

“It’s not unprecedented to have the Justice Department weigh in on the appropriate use of the money,” Antonia M. Apps, a lawyer with Milbank, Tweed, Hadley & McCloy and a former federal prosecutor for the Southern District of New York, said. “The scale of this corruption case is much larger than your typical corruption case, so the dollars are greater than you would normally see.”

As American authorities announced their case in 2015 and dozens of powerful officials and marketing executives pleaded guilty to charges including racketeering, wire fraud and money laundering conspiracy, prosecutors made clear they saw the soccer organizations as victims that had been co-opted by dishonest operators.

Lawyers for FIFA and the regional confederations were quick to embrace that view, and fought further to manage the perceptions of prosecutors and the public by seeking to distance the organizations from the accused criminals, both by cooperating with the authorities and to solidify the sports organizations’ role as victims, powerless to their top leaders’ fraud.

In a court filing in 2016, lawyers for FIFA argued that the organization had lost at least $28 million paid to 20 soccer officials over 12 years, along with having suffered other incalculable costs.

CONMEBOL, the South American confederation, has already recovered millions of dollars through other channels. In July, it said it had been awarded more than $1.7 million by the Swiss authorities — money that had been in a personal account of one of its former leaders. That came in addition to the $55 million the organization said it had clawed back from the accounts of other former officials.

In the years since the FIFA corruption scandal burst into public view with raids on a luxury hotel on the eve of a FIFA congress in 2015, the case, one of the largest criminal prosecutions in America when it was announced, has moved forward even as public attention to its proceedings and to corruption in global soccer has waned.

Just this week, Reynaldo Vasquez, El Salvador’s former top soccer official who was charged in 2015, pleaded guilty in federal court in Brooklyn. And earlier this year, prosecutors announced the Swiss bank Julius Baer had agreed to pay more than $79 million in penalties for its role in laundering money in the scandal.

Even so, years on, key figures await sentencing, and some former officials remain at large. One, Marco Polo Del Nero, the former head of Brazil’s soccer federation, was recently recorded appearing to direct the federation’s affairs despite having been barred for life by FIFA from working in organized soccer.

But in announcing a new conviction this week, American law enforcement officials telegraphed that they were still keeping tabs on the sport. Tuesday’s announcement underscored that.

“From the start,” the acting U.S. attorney for the Eastern District of New York, Jacquelyn M. Kasulis, said in a statement, “this investigation and prosecution have been focused on bringing wrongdoers to justice and restoring ill-gotten gains to those who work for the benefit of the beautiful game.”