"Aware of the critical situation our country is currently facing, and given my responsibility as chairman... I decided to resign with immediate effect," Hildebrand said at a press conference in Bern.
Hildebrand published emails on the SNB website to show he had no knowledge of the transaction until after the fact, but in resigning he said he was unable to "to provide irrefutable evidence" to totally prove his innocence.
Press reports claimed last week that Hildebrand's wife Kashya profited after buying $504,000 last August, just weeks before an intervention by the SNB to halt the rise of the franc -- a move that saw the dollar rise significantly against the Swiss currency.
"I failed my husband by not considering the perception of a 'conflict of interest' created by my purchase of dollars," Ms Hildebrand said in a statement issued on Monday.
The scandal took a political turn with revelations that the government last month received banking documents concerning Hildebrand's personal trades from Christoph Blocher, chief of the conservative Swiss People's Party (UDC), the largest in the Federal Assembly.
The Swiss weekly Weltwoche, close to the UDC, charged the controversial currency trades were made by Hildebrand and not by his wife without his knowledge, as the central bank had indicated.
Last week Hildebrand insisted he would not step down.
"So long as I have the confidence of the government and the bank council, stepping down is not an issue for me," Hildebrand had said, but Swiss media speculated on Monday the bank's governing body was coming under pressure.
Hildebrand's announcement came despite backing at the weekend from Swiss President Eveline Widmer-Schlumpf who said he should not resign.
On Monday, however, the Swiss Federal Council that governs the country said the "stability and credibility of the SNB are essential for the economy and the good of the country."
It said in a statement it regretted "the developments of the situation that led to the resignation" and thanked Hildebrand, saying he had "demonstrated great expertise in monetary policy, especially in times of crisis."
After Hildebrand stepped down the SNB said it will continue to defend "with the utmost determination" the exchange rate floor of 1.20 francs a euro.
"The current monetary policy on the SNB exchange rate of a minimum of 1.20 francs a euro remains unchanged," the central bank said in a statement, adding it "regretted the decision and the circumstances" that led Hildebrand stepping step down as chairman.
The SNB said Vice Chairman Thomas Jordan would take over as chairman from Hildebrand.
With his departure as head of the central bank, Hildebrand also stepped down as vice president of the Financial Stability Board (FSB), an organisation charged with reforming the international banking system.
Mark Carney, Chairman of the FSB, said "Philipp has been instrumental in helping to manage the response to the global financial crisis and in developing major reforms to strengthen the resiliency and stability of the international financial system."
At the news conference Hildebrand defended his professional record at the helm of the central bank following the financial crisis of 2008.
"I would like to think I have been a damn good central banker," Hildebrand said while noting he had "advocated strongly and early for stricter capital requirements for the big banks."