Ed Kahrer, an assistant special agent in charge of the FBI's white collar crime and public corruption programme in New Jersey, called corruption "a cancer that is destroying the core values of this state".
"New Jersey's corruption problem is one of the worst, if not the worst, in the nation," Kahrer, who has worked on the investigation since it began in July 1999, said.
"It has become ingrained in New Jersey's political culture."
Investigators used an informant, a real estate developer charged with bank fraud three years ago, to uncover a money laundering ring and organ trafficking, as well as corruption by politicians who exploited loopholes in state law to disguise bribes as campaign contributions.
Peter Cammarano III, mayor of Hoboken, New Jersey, accused of accepting $25,000 in cash bribes
Dennis Elwell, mayor of Secaucus, New Jersey, charged with taking $10,000
Anthony Suarez, mayor of Ridgefield, charged with agreeing to accept an illegal $10,000
Leona Beldini, deputy mayor of Jersey City, charged with conspiracy to commit extortion by taking $20,000 in illegal campaign contributions
Daniel Van Pelt and L Harvey Smith, both state assemblymen, accused of taking payoffs
The politicians arrested in the investigation were not accused of any involvement in the money laundering or the trading in human organs.
The money laundering network is alleged to have laundered tens of millions of dollars through Jewish charities controlled by rabbis in New York and New Jersey.
They laundered some $3m for the undercover witness between June 2007 and July 2009, authorities said.
Investigators raided several synagogues and among those arrested was Saul Kassin, the chief rabbi of Syrian Jews in the US.
Those arrested also included Levy Izhak Rosenbaum, a Brooklyn rabbi, who was charged with conspiring to arrange the sale of an Israeli citizen's kidney for $160,000 for a transplant for the informant's fictitious uncle.
Rosenbaum was quoted as saying he had been arranging the sale of kidneys for 10 years.
Ralph Marra, the acting US attorney, told a press conference that the sweep demonstrated "the pervasive nature of public corruption in this state".
"The politicians willingly put themselves up for sale," he said, while "clergymen cloak their extensive criminal activity behind a facade of rectitude".
US television footage showed FBI and tax agents bringing a stream of handcuffed suspects, including the rabbis wearing traditional Orthodox Jewish garb, into custody in the city of Newark.
Most of the defendants facing corruption charges were released on bail.
The money laundering defendants faced bail between $300,000 and $3m, and most were ordered to submit to electronic monitoring.
New Jersey has long been notorious for official corruption and organised crime and is best known as the setting for the popular television show "The Sopranos".