Jorge Luis Arzuaga, a former managing director at the Swiss bank Julius Baer, pleaded guilty to money laundering conspiracy in Brooklyn federal court on Thursday, revealing his role in the United States’ sweeping criminal case focused on FIFA, the governing body of international soccer.

Mr. Arzuaga, who admitted to arranging the financial transfers of more than $25 million in bribes and kickbacks from 2010 to 2015, became the first banker publicly convicted in a case that has felled dozens of soccer officials and marketing and media executives since it was announced two years ago. His conviction suggests a new phase for the case, shifting its focus to the financial institutions through which bribe money traveled.

The Swiss have pursued similar charges against Mr. Arzuaga, the United States Justice Department said Thursday, and a resolution is expected to be announced soon. The conviction of Mr. Arzuaga, a citizen of Argentina who worked for the Zurich bank until 2015, would be Switzerland’s first in its parallel investigation into FIFA, which has its headquarters in Zurich. Switzerland’s Office of the Attorney General did not immediately respond to a request for comment Thursday.

Over the last two years, the Swiss authorities have provided significant assistance to the United States in carrying out arrests, extraditing defendants and responding to requests for information otherwise protected by the nation’s strict privacy laws. Switzerland’s Office of the Attorney General announced its own investigation into FIFA, after early-morning raids at a five-star hotel in 2015 that resulted in the first wave of arrests and upended soccer’s global leadership.