Stephen, a former Olympic weightlifter who had been in power since December 2007, will be replaced by Freddie Pitcher, a former minister of commerce, industry and environment, the Sydney Morning Herald said on its website.
The reported move came after opposition member David Adeang last month used parliamentary privilege to read out what he said was correspondence between Stephen and a phosphate dealer in Thailand.
Stephen allegedly asked in an email for a kickback on the sale of 25,000 cubic tonnes of the mineral.
The Sydney Morning Herald said Adeang last week tabled a motion of no confidence against Stephen which was due to be heard Thursday, but the president resigned instead.
“He has done the honourable thing to resign but we would have thought it would have been more honourable if he had resigned earlier,” Adeang said according to the daily.
Nauru is one of the smallest nations in the world with less than 10,000 residents.