Saudi Arabia and other pro-American countries in the Arab world were jubilant today over the U.S. Senate approval of the controversial sale of five Airborne Warning and Control System (AWACS) planes to the Saudi kingdom.

Some saw it as a turning point in American-Arab -- as well as American-Israeli -- relations, and others said the Reagan administration had won a battle that clearly stood to affect U.S. credibility in the Arab world for years to come.

In Riyadh, the Saudi defense minister, Prince Sultan ibn Abdel Aziz, expressed his "thanks and appreciation" to President Reagan and "deep gratitude" to Americans who worked for approval of the sale.

"The Saudi people will undoubtedly never forget this stand by the friends" who helped them, Sultan told a press conference in the Saudi capital.

The AWACS deal, he said, was "completely in line with Saudi Arabia's sovereignty and national dignity" and was intended solely for the defense of "this holy country."

His remark appeared to be a reference to the understandings Saudi and U.S. officials reached over the use of the planes and the kind of equipment they are to carry.

Within hours of the Senate vote, the U.S. ambassador to Saudi Arabia, Richard Murphy, delivered a message from Reagan to King Khalid, the Saudi state radio reported. There was no indication what the message said, but it presumably dealt with the AWACS vote and future U.S.-Saudi cooperation.

Saudi newspapers, which are state-controlled, hailed the outcome as a great victory for the kingdom, the United States and the whole Arab people.

"We congratulate ourselves and our friends in the United States because the Saudi will has been able to achieve a major political victory not merely for itself but for the Arab people everywhere," said an editorial in Al Jazira. "The success of the deal made the American citizen able to balance between his national interests and the pressure forces."

Reagan was called one of "the greatest American leaders in recorded history," who had realized that "the strength of Zionist influence is nothing but a wooden horse that can be broken when America comes first."

Reagan is viewed within the Arab world as having stood up to Israeli opposition to the $8.5 billion sale. The Israelis are widely perceived within the Arab world as having almost paramount influence over the U.S. political scene.

Here in Egypt, where two AWACS planes are stationed as a show of U.S. support in the aftermath of the assassination of Anwar Sadat, the reaction was just as jubilant.

Foreign Minister Kamal Hassan Ali called the vote a "positive turning point in relations between the United States and the Arab nations" that would help Egypt's allies defend themselves against foreign intervention.

Noting that Sadat long had advocated the sale and even sent then-vice president Hosni Mubarak to Washington to lobby for it, Ali said the successful outcome would "push forward the peace process by great leaps."

A State Department official announced today that the two AWACS planes sent here shortly after Sadat's assassination Oct. 6 were being withdrawn in two days.

The official said the decision to withdraw them had been made "after consultation with the Egyptian government" and said both had concluded "that the operation and training missions of this particular exercise have been served and that the planes can be withdrawn at the end of the month."

Earlier, both Egyptian and U.S. officials had said the AWACS planes would stay to participate in the joint military maneuvers the two countries are planning to hold here next month.

Another close U.S. ally, President Jaafar Nimeri of Sudan, also acclaimed the Senate approval of the sale to Saudi Arabia.

Hailing Reagan's "wise leadership," Nimeri said in a message to the White House: "On this occasion we convey to you, dear friend, our warmest congratulations and deep appreciation for all the efforts you have done to accomplish this noble task, which will enable Saudi Arabia to play its role as a leading state in the area."

Both Sudan and Egypt asked for an acceleration of U.S. arms shipments to their countries following Sadat's assassination partly out of fear of increased subversive activities by Libya, whose leader, Muammar Qaddafi, is a strong foe of the two U.S.-backed governments.

One of the purposes of the AWACS planes sent here was to improve Egyptian and Sudanese intelligence along their frontiers with Libya. Since their arrival, both Egypt and Libya have announced a pullback of forces along the border.

Soviet-backed Syria, one of the leading Arab critics of the AWACS sale, complained that the restrictions placed on the planes rendered them useless to the Arab cause.

Al Baath, the newspaper of Syria's ruling party, criticized the understandings outlined by Reagan to win Senate approval, notably that the planes would not be used against Israel and that the United States would have a role in their operation into the 1990s.

"The answer to the puzzle of these strings might be much more dangerous than the question," the Syrian paper said.