It is understood Wise, 57, will step down as CEO after his successor is chosen, but will remain as chairman through till the end of the year.
The resignation of Wise is a major victory for dissident shareholder and natural gas tycoon Oscar Wyatt, who for months has railed for a change in top management and accused the company of engaging in a host of financial manipulations at the expense of its stockholders.
El Paso has also agreed to pay $15.5 million to California energy customers to settle charges that it helped Enron Corp manipulate the state's energy market to drive up prices. El Paso was accused of helping Enron in the "ricochet" deals in 2000, where Enron transferred electricity out of California to El Paso, then sold it back into the state, avoiding price caps.