David Owen, a 38-year-old moderate, tonight succeeded Anthony Crosland as Britain's foreign minister.

He is the youngest secretary since Anthony Eden, then two months younger than Owen is now, took charge of foreign affairs here in 1935. Britain was then a major world power. Today, its influence in global matters is marginal. Even so, this is a stunning promotion for Owen, a physician, who has been No. 2 at the Foreign Office.

He stands on the Labor Party's right wing. But, like Prime Minister James Callaghan who appointed him, Owen has been careful to keep on good terms with the left.

Owen's most notable contribution to foreign affairs was his resignation from Labor's front bench five years ago over the party's opposition to Britain's entry into the Common Market. His appointment was greeted with applause in Brussels, the Common Market headquarters.

Like his predecessor Crosland, who died Saturday, Owen masters masses of material easily, is more pragmatic than doctrinaire, glitters with charm and is married to an American, the former Deborah Schabert, a literary agent. They met while Owen, then in his third year in Parliament, was watching Eugene McCarthy's 1968 campaign in New Hampshire.

Owen is a product of Britain's upper middle class. The son of a doctor, he went to a private school, Cambridge and St. Thomas Hospital. Not long after he completed his medical training, he was appointed to a key post at St. Thomas, neurological and psychiatric registrar.

A strikingly handsome man, his rise to a top Cabinet post has been extraordinarily rapid. He does not like to be categorized as left or right and prefers to call himself a "Welsh-liberal-radical."

How long he will hold his new post is a question, although Callaghan's spokesmen stressed tonight that Owen is not merely keeping the seat warm for somebody else.

The somebody else is Denis Healey, who is eager to leave his disaster-ridden career as chancellor of the Exchequer and take over the Foreign Ministry. Healey, however, must first preside over another budget in March to reverse the deflationary impact of his last venture in December. Healey is also counted on to work out another and difficult deal with the trade unions, curbing pay increases.

Healey was to switch posts with Crosland this summer, but now his hopes may be doomed. In any event, the whole question could be academic since Callaghan's government is beginning to look like it is coming apart. The Conservatives appear to be easy winners of any election in the next few months.

Healey got one consolation. His No. 2 at the treasury, Joel Barnett, was promoted to Cabinet rank. Healey has been saying that Barnett would make a good successor at the treasury if and when Healey moves to the Foreign Office.

Callaghan, mindful that the party's left should receive a token when the right carries off the top positions, provided one in Judith Hart, a leftist stalwart, who returns to the Cabinet in charge of Britain's shrinking foreign aid program. She had held this post before under Harold Wilson, but resigned, largely because of his conservatism.

In his first bid for a Labor seat in Parliament, in 1964, Owen lost but in the 1966 general election he narrowly won the Labor seat he still holds in Plymouth. A year later, at the age of 28, he was appointed Navy minister, a non-Cabinet post.

When Labor was returned to office under Wilson in 1974, Owen became a junior minister at the Ministry of Health and Social Security.

As minister of state at the Foreign Office -- a post he was appointed to last September by Callaghan -- Owen stood in for Crosland during his illness last week and two days ago flew to Brussels to lead a Common Market team in negotiations with the Soviet Union on fishing rights.