President Reagan announced yesterday that a 46-year-old bank examiner from Atlanta was the "mystery hero" of last year's Air Florida crash -- the man who passed a lifeline to others before drowning in the ice-covered Potomac River.

The president disclosed that a Coast Guard investigation determined that Arland D. Williams Jr., an employe of the Federal Reserve system, "was the hero who gave his life that others might live.

"You can live with tremendous pride. . . ," Reagan told Williams' parents and his two children as he posthumously awarded Williams the Coast Guard's Gold Lifesaving Medal at a ceremony in the Oval Office. Reagan quoted from a Time magazine article after the Jan. 13, 1982, crash, saying: "If the man in the water gave a lifeline to the people gasping for survival, he was likewise giving a lifeline to those who observed him."

The award came after Williams' mother, Virginia Williams of Mattoon, Ill., wrote to the president asking if something could be done to resolve the question of whether her son was, as some news accounts had suggested, the unknown passenger who had been seen giving a helicopter rescue line to others. "I ask no honors. But I do ask that he be acknowledged as a hero, not the unknown hero," she said.

Mrs. Williams came to Washington to receive the medal along with her husband and her son's two children, Leslie and Arland III. After the ceremony, she said: "I'm very appreciative that it has been determined that it was Arland and that there will no longer be an unknown hero . . . . It doesn't bring him back, but it helps."

Seventy-eight persons were killed when an Air Florida 737 jetliner bound for Tampa hit the 14th Street bridge during a blinding afternoon snowstorm and plunged into the river.

Six of the plane's passengers managed to reach the water's surface, where they clung to wreckage and cried for rescue. A U.S. Park Police helicopter arrived with a lifeline, which was dangled to survivors in an attempt to drag them toward the shore.

The helicopter's crewmen reported that a man in the water repeatedly passed the line to other survivors. They described him as bald, with graying hair on the sides of his head and a graying mustache. He did not have a beard, they said. When the helicopter returned to him, they said, he had sunk into the water and could not be found.

Uncertainty arose because one of the survivors, Joseph Stiley, said that he had not seen anyone repeatedly and heroically passing a lifeline as the wreckage sank into the river. Stiley said he was in the water near a man who said he was "strapped in a seat and can't move" and did help Stiley propel a line toward another survivor.

Early speculation had centered on Williams because autopsies showed that he was the only victim who died of drowning and exposure, not injuries from the impact. But Williams had a beard, conflicting with the helicopter crew members' description.

As Lenny Skutnik, the bystander from Lorton who leapt into the frigid water to rescue a woman who was about to sink, and others involved in the rescue were acclaimed as heroes, interest arose in the media and elsewhere into establishing the identify of the unknown man.

The D.C. Police Department pored over the evidence and concluded that the "most probable" answer to the puzzle was Williams. "The trauma for all the other victims was of such a severe nature that they probably could not have been that unknown hero," said Lt. William Ritchie of the homicide squad.

A Coast Guard study initially recommended awards for a lifesaving award members of the rescue helicopter crew, for Skutnik, Roger Olian, who also plunged into the river, and for the unknown man who passed the rescue line to others. In November the agency reopened its investigation at the White House's request and reached the conclusion that Reagan disclosed yesterday.

The citation, which accompanied Williams' medal and was signed by Transportation Secretary Elizabeth Dole, credited him with "extreme and heroic daring."

He was seated in the rear of the plane, the citation said, which was still partially above the water when the rescue helicopter arrived. "Mr. Williams, although injured, quickly realized that he was trapped in his seat by a jammed seat belt," the citation said.

"Mr. Williams sacrificed his own life so that others may live. Mr. Williams' unselfish actions and valiant service reflect the highest credit upon himself and were in keeping with the highest traditions of humanitarian service," the citation said.

Rep. Dan Crane (R-Ill.), who represents Mattoon, introduced a resolution in January in the House of Representatives calling for Williams to be declared a "national hero who made the ultimate sacrifice."