Joe L. Allbritton took full control of Riggs National Bank yesterday.

Allbritton, who paid $70 million in 1981 to buy 40 percent of the stock in Washington's biggest bank company, became chairman and president of the bank at a reorganization meeting yesterday. Since April 1981, Allbritton has been chairman of Riggs National Corp., the holding company whose only asset is the $3.7 billion bank.

Allbritton's consolidation of his power over the bank itself came at the same time that Riggs announced that its profits declined nearly 17 percent in 1982, from $24.4 million ($3.39 per share) in 1981 to $20.3 million ($4.07) last year.

Riggs' declining earnings reflects both the sharp increase in problem loans to foreign borrowers and real estate developers and the costs of selling off its money-losing Central Charge Service Inc. Riggs said that increasing its normal provision for bad loans and selling Central Charge cost the bank $5 million after taxes. Riggs lost $1.1 million on securities sales last year. It had no securities gains or losses in 1981.

In assuming the posts of chief executive and president, Allbritton takes over responsibilities previously handled by former bank chairman Vincent C. Burke Jr. and President Daniel J. Callahan III.

Callahan, who has been the bank's chief operating officer since 1976, will continue as president of Riggs National Corp., but will lose all day-to-day operating authority over the bank.

Sources close to Riggs said Callahan is expected to leave the bank soon. The official press release from Riggs said Callahan will preside over "the future development and expansion of Riggs National Corp."

In September, Allbritton stripped Burke of his duties as chief executive officer of the bank. Last Monday Burke resigned from the ceremonial position of chairman to join the Washington law firm of Steptoe & Johnson.

The announcement of Allbritton's consolidation yesterday is the latest in a series of management shakeups at the venerable Washington banking institution. Sources at Riggs and in the banking community said that Allbritton's dissatisfaction with the bank's declining profits and rising problem loans prompted a major housecleaning.

Sources said yesterday that William G. Tull, one of the bank's three executive vice presidents, has resigned to take a job in another state. Tull did not answer a reporter's phone calls.

Other recent departures include James D. M. McComas, who headed Riggs' international lending operations until he resigned last September. McComas now heads his own consulting firm.

Last week, Webb C. Hayes IV resigned to become president of Palmer National Bank, a new bank that expects to open its doors here next May. William C. Moreland was removed as head of the bank's marketing division.

Thomas W. Wren, who is president of University Bancshares in Houston, which Allbritton also owns, was elected vice chairman of the Riggs Bank board yesterday. The bank did not reveal what additional duties--if any--Wren will have in that post. He already was vice chairman of the parent company.

Sources close to Riggs said yesterday that several other senior executives can be expected to resign or be reassigned within the next few weeks as Allbritton moves to change the direction of the bank. "The level of executive paranoia has reached new heights there," said a top official at another Washington bank.

The performance of Riggs in recent years has been a stark contrast to Washington's second biggest bank company, American Security, which has assets of $3.4 billion compared with Riggs' $3.7 billion.

Profits at Riggs declined slightly in 1981 before taking a large dip in 1982. Last year's profits are lower than in 1979, although Riggs has nearly $1.4 billion more in assets than it did in 1979.

American Security, on the other hand, has reported steady earnings increases each year and reported its 1982 net income grew 10.9 percent to $30.1 million before securities transactions.