Myer Rashish has resigned as undersecretary of state for economic affairs, ending a three-month saga of struggle and rumor, informed sources said yesterday.

The resignation of Rashish, which is effective next Thursday, is to be announced by the White House shortly, the sources said.

As long ago as early October, Secretary of State Alexander M. Haig Jr. was publicly reported to be unhappy with Rashish and planning to replace him. The stories were never authoritatively denied, but Rashish remained in his job, apparently supported by some White House officials.

Despite the common knowledge that Haig, for reasons that were never plainly stated, was pushing for the resignation of his senior economic aide, Rashish attended the North-South summit meeting at Cancun, Mexico, and other international meetings and saw foreign diplomats.

Several weeks ago Haig reportedly demanded that Rashish vacate his job before Jan. l, but it was unclear at that time that he had obtained White House backing for the demand. Subsequently the White House notified Rashish that President Reagan had acceded to the demand by Haig, and a date was set.

Under present arrangements, the Washington economist is not expected to take another government post, but will return to private life.

Haig's choice to succeed Rashish is Robert D. Hormats, who has been serving one rung down on the bureaucratic ladder as assistant secretary for economic affairs.

Despite reports of some congressional opposition, Hormats is generally expected to get the job, especially because his present post is to be filled by Richard T. McCormack, a former staff member of Sen. Jesse Helms (R-N.C.)

McCormack has been occupying an office next to Hormats for well over a month as a paid consultant to the State Department's economic bureau while awaiting the shuffle.