Mr Overton, 39, announced his departure on Twitter, where he had written that a "very senior political figure" would be exposed as a paedophile on November 2, hours before the report was broadcast.
Tory backbencher Andrew Bridgen used a parliamentary motion to call on the funders, which include Oxfam, Save The Children and the Joseph Rowntree Trust, to cut all ties with the bureau. He said it was now "totally discredited as a serious producer of quality journalism".
It was created in 2010 and is based at London's City University as an independent and not-for-profit operation.
It produces investigations for press and broadcast media, working in collaboration with other news groups with the "aim of educating the public and the media on both the realities of today's world and the value of honest reporting".
James Lee, chairman of the bureau's trustees, said it was "launched and built up under Iain's editorship". He described Mr Overton's resignation as a "real tragedy".
"Iain has played a pivotal role in the bureau's success to date. Under his editorship the bureau has gained a reputation for quality journalism as well as winning awards," he added.
In 2004, Mr Overton won a Scottish Bafta for the expose Security Wars, a film about corruption in the Scottish security industry.
The bureau has also worked with Panorama and Channel 4 News and has won a number of journalism awards.
It said an inquiry had been established to examine the Newsnight story.