Walter J. Stoessel Jr., the third-ranking official of the State Department, will succeed William P. Clark as deputy secretary of state, with Lawrence S. Eagleburger replacing Stoessel as undersecretary for political affairs, the White House announced yesterday.

The promotion of Stoessel and Eagleburger, now assistant secretary for European affairs, will put career foreign service officers in the second- and third-ranking jobs at State for the first time since the department's bureaucratic structure underwent considerable expansion in the postwar period.

The decision to move up Stoessel and Eagleburger was motivated in part by the desire of Secretary of State Alexander M. Haig Jr. and Clark, who on Monday was named President Reagan's national security affairs adviser, to make a morale-boosting gesture of recognition toward the foreign service, senior administration sources said.

The sources said Haig's recommendation initially encountered resistance at the White House, where some officials reportedly wanted to continue the tradition of reserving the deputy's slot for an outside political appointee. But Clark, in one of his first moves in his new post, convinced Reagan that the appointments would be a wise step, the sources said.

The White House also announced that Powell A. Moore, Reagan's deputy legislative affairs assistant, will move to State as assistant secretary for congressional relations. Richard Fairbanks, who holds that post, is expected to become a special assistant to Haig, the sources said.

In addition, the sources continued, Thomas O. Enders, another career officer currently serving as assistant secretary for inter-American affairs, is under consideration to succeed Eagleburger.

They also said that Rozanne L. Ridgway, who served as counselor of the department in the last months of the Carter administration, is being considered for the vacant post of assistant secretary for international organization affairs, although the sources added there is opposition within the administration to her appointment.

Meanwhile, Reuter news agency reported yesterday that at a meeting last month, Haig delivered an angry tirade against Myer Rashish, undersecretary for economic affairs, and demanded that he resign or be fired by Jan. 1. However, Reuter added, the White House failed to back Haig up, and Rashish is still on the job.

It has been known for months that Haig has been dissatisfied with Rashish's performance and wants to replace him with Robert D. Hormats, the assistant secretary for economic affairs. Administration sources say, though, that the proposed change has been held up by opposition to Hormats from some officials at the White House and Republican conservatives in Congress.

Stoessel, who will be 62 on Jan. 24, is the senior member of the foreign service. His 40-year diplomatic career has focused almost exclusively on Europe, and before becoming undersecretary at the outset of the Reagan administration he served as assistant secretary for European affairs and ambassador to Poland, the Soviet Union and West Germany.

Eagleburger, 51, who is hospitalized with a leg ailment, also is a European affairs specialist. He was ambassador to Yugoslavia from 1977 to 1980. Although Haig is known to regard him as an especially valuable aide, his appointment as assistant secretary last year initially encountered opposition from Sen. Jesse Helms (R-N.C.) and other Republican conservatives who objected to Eagleburger because he was regarded as a protege of former secretary of state Henry A. Kissinger.

Eagleburger is understood to have given notice last month of his intention to leave the foreign service to accept a high-paying position in private business. However, the sources said, he decided to remain after being offered the undersecretary's post, which traditionally has involved day-to-day management of the department's principal dealings with foreign governments.

Both Stoessel and Eagleburger have had major roles in formulating and carrying out the U.S. response to the Polish crisis. In addition to being close to Haig, they enjoyed a good working relationship with Clark during his 11 months at State, and their promotions are likely to be of significant help to the new national security adviser in his efforts to bring about a more coordinated and harmonious working relationship between the White House and the State Department.

Administration sources also said that at a meeting yesterday with members of the National Security Council staff Clark ordered them not to talk with the press or make any public statements not specifically authorized by his office for 60 days.

The order reiterated a rule originally imposed under Clark's predecessor, Richard V. Allen, but enforced with relative laxity in recent weeks.