Unable to get a clear commitment from the Reagan administration on a proposed purchase of F15 fighters for its Air Force, Saudi Arabia has decided to purchase 48 British-made Tornado combat jets as part of a $3 billion arms package, authoritative British sources here and U.S. sources in Washington have disclosed.

The deal, which the Saudis are undertaking after receiving an explicit green light from President Reagan to buy non-U.S.-manufactured equipment, will mark one of Britain's largest arms sales ever and results in part from an intensive personal sales campaign by Prime Minister Margaret Thatcher.

The British sale is certain to stir controversy. According to British officials, Britain will not impose conditions on how the fighter planes will be used or where they may be stationed in Saudi Arabia, as the United States was prepared to do in deference to Israeli security concerns.

Also, the sale reportedly will be financed in part by the barter of Saudi oil to Britain for remarketing abroad. Saudi Arabia's partners in the Organization of Petroleum Exporting Countries (OPEC) have previously strongly resisted barter sales of this kind.

The agreement is to be signed later this month when the Saudi defense minister, Prince Sultan ibn Abdul Aziz, visits London. Its completion effectively will mean an end to the Reagan administration's efforts to sell 40 to 50 F15s to the Saudis this year, since military analysts report that Saudi Arabia's small military establishment would have extreme difficulty in absorbing both purchases.

The official Saudi press agency reported the deal today in a brief statement, according to The Associated Press. It said the accord was in line with the kingdom's plan to "diversify the source of its arms" and involved jet fighters and other equipment for the air force, but it gave no details.

A British official said that although the United States long has been the Saudis' principal arms supplier, particularly to the Air Force, the "American option" on the new jets had been eliminated as a "front-runner" by midsummer. It was at this point that the Saudis indicated strong interest in the Tornado package and Thatcher intensified her involvement.

The official noted that as a result of recent "correspondence between the White House and the royal family" in Riyadh, "the British are reassured" that the United States would not object to the Saudi decision to go ahead with the British deal, which also includes 20 Hawk trainer fighters.

In addition to the White House reassurance, believed to have come in a letter from Reagan to Saudi King Fahd, sources here said that the deal was spurred by the personal salesmanship of Thatcher.

Thatcher met with Fahd last spring, when she made a brief stop in Saudi Arabia on her return from a trip to Southeast Asia. In addition, she has written "one or two letters" to him, and broke into her vacation last month to hold a secret meeting with Sultan in Austria.

British Defense Secretary Michael Heseltine also made three visits to Saudi Arabia during the past year to discuss the sale.

"We couldn't say that Reagan steered" the Saudis in Britain's direction, a source here said. "We like to think, and Mrs. Thatcher likes to think, that we all have a close relationship. Certainly in a political sense, this government, Reagan and the Saudis are all very close."

"There is a political dimension," the source said. "It's a classic example of where personal relations play a part."

Thatcher also became deeply involved this month in trying to get the White House and Pentagon to overturn a recommendation by the U.S. Army that a $4.5 billion communications contract be given to a French defense contractor rather than to a British firm, and she has pressed Indian Prime Minister Rajiv Gandhi to reverse an earlier decision to cancel the purchase of Westlands communications helicopters.

The British sale of sophisticated jet fighters to Saudi Arabia also beats out a longstanding bid by France, which was reportedly on the verge of clinching a deal last spring to sell a similar number of Mirage 2000s to the Saudis. The agreement reportedly fell through because of the insistence by Saudi Arabia, which is short of readily available cash reserves, that at least half the price be paid in oil.

British sources, noting the French experience, cautioned that their sale to the Saudis will not be complete until the contract actually is signed. But they said that senior Saudi officials are in London to make final arrangements and that Saudi defense representatives have been working here with Britain's Royal Air Force on the package for several months.

The sources said that a "planning date" had been reached for Sultan to visit here and sign "around the end of next week."

The British sale also will include some payment in oil, which Britain, itself an oil producer, likely will sell. Referring to it as "Saudi gold," a source here said that "a lot of these deals have a barter content. That will certainly be part of it, but we don't actually have to take the oil."

The Tornado is produced by a British, Italian and West German consortium, but the planes are assembled and marketed by state-owned British Aerospace. Outside sales of the plane have been disappointing until this summer, when Oman purchased eight of the jets, which can be assembled in either a ground attack or air defense configuration.

Saudi military officials had made clear their preference to buy new F15s to augment the 62 McDonnell Douglas planes they bought after a bruising fight between the Carter administration and Congress in 1978. The F15 is a twin-engine, single-pilot aircraft well-suited to the long air patrols and difficulties in maintenance experienced in Saudi Arabia. The Tornado is more useful as a ground attack aircraft than as an interceptor, the primary role Saudi Arabia has assigned to the F15.

British officials speculated that a recent decision by Britain, Italy, West Germany and Spain to build a new combat plane due to be available in the mid-1990s helped sway the Saudis toward the Tornado in the interests of keeping their options open for future continuity in defense purchases.

The Saudi purchase of the Tornados constitutes a marked departure in the strong defense procurement relationship between Washington and Riyadh, which had purchased U.S. military aircraft almost exclusively since the early 1960s. But those purchases increasingly have been the subject of strong congressional opposition on the ground that the Islamic kingdom could pose a serious threat to Israel in the event of another Arab-Israeli war.

The F15 sale in 1978 passed the Senate by a 55-to-44 vote only after acrimonious debate. The sale was conditioned on a Saudi promise not to base the planes at Tabuk Air Base in the northwest corner of the kingdom, within easy range of Israel.

The Saudis long have been seeking to replace obsolete British-made Lightning jets stationed in Tabuk with an advanced fighter like the F15. Ironically, the British were able to make the Lightning sale to Saudi Arabia with the direct encouragement of the Kennedy administration, which understood that Britain would use the money from the sale to purchase U.S.-manufactured fighter aircraft for the Royal Air Force.

That sale was not completed, however, and U.S. firms complained bitterly to the Saudis about the Lightning purchase. The Reagan communication to the Saudis cited by British officials here may be an effort to prevent any recriminations from disappointed American defense manufacturers.

"We are disappointed they couldn't wait," a Pentagon official said in Washington. This official indicated that the administration had concluded earlier this summer that continuing to push for the Saudi package would endanger a separate push to provide more arms to Egypt and Jordan.

Secretary of Defense Caspar W. Weinberger carried to Saudi Arabia in December a letter from Reagan containing a qualified but unmistakable commitment to the Saudis to provide 40 to 48 F15s, according to U.S. sources, but the failure of Secretary of State George P. Shultz and national security adviser Robert C. McFarlane to support the sale actively this summer caused it to falter.

The administration put together a package of arms sales that included two squadrons of F16s or F20s and mobile improved Hawk antiaircraft missiles for Jordan. On Thursday, Shultz told a group of Jewish members of the House that the administration was determined to push ahead with the sale to Jordan.

In addition to the absence of the Tabuk restriction, the British deal has the advantage of being able to provide the first shipment of as many as 20 Tornados within 18 months of signing. Those planes would replace the Lightnings with a Tornado squadron. The F15s would not have been delivered until 1989.

Sources here said that talks between Saudi defense representatives and Britain's Air Force have been under way for several months over how the air-combat planes will be outfitted and what spare parts and avionics will be included in the package.

The contract, including the Tornados and the Hawks, will be a long-term one, spanning as long as 20 years including supply, spare parts and training. But planes for the first shipment of Tornados, at a price of about $21 million to $28 million each, already are being assembled, sources here said. CAPTION: Pictures 1 through 3, The Tornado is used as a ground attack plane; The Saudis have used the F15s as interceptors; Britain's $3 billion sale, approved by Reagan, results in part from an intensive personal sales campaign by Prime Minister Thatcher.