Jim Brady came back to the White House press office yesterday, 224 days after he last left it to accompany President Reagan to a speech at the Washington Hilton Hotel.

He returned grinning, giving a thumbs-up sign to reporters and White House staff members who cheered and applauded at what for most was their first glimpse of Brady since a would-be assassin's bullet ripped into his brain.

"Jim, we're all waiting for the day you're back for good," Reagan said at a brief, emotional ceremony.

"I am too, Mr. President," Brady responded.

Brady's voice is extremely high and his diction less precise as a result of the bullet's damage, but from the moment he entered the press room, Brady demonstrated that he has lost neither his wit nor his good humor.

"Hello, good friends," Brady said as he was wheeled into the room to loud applause from more than 100 people. "We miss you, Jim," a reporter said. Brady gave the automatic reply: "I miss you." Then he looked around the room and amended his thought: "I miss most of you."

He spotted Sam Donaldson of ABC, who had been outside with a crew to photograph Brady's arrival at the White House. "We tried to run over Sam in the street," Brady joked.

Reagan began with a series of one-liners marking the return of reporters and press office staff members to the West Wing of the White House after a three-month renovation during which they were housed across the street in the Executive Office Building.

The press room is built over a swimming pool, Reagan reminded the crowd, but "it isn't true that the floor is hinged."

"Yes it is," Brady interjected to loud laughter.

One of the bullets meant for Reagan March 30 struck the president in the left lung. A Secret Service agent and a D.C. policeman also were wounded, but Brady, who fell face down on the sidewalk and lay almost motionless as the blood ran from his head, was the most grievously injured in the shooting.

After his joking introduction yesterday, the president turned serious. Brady's "courage has been an inspiration to all of us," he said of the man who was so gravely wounded that doctors first thought he had little chance of survival.

Brady, 41, beat the earliest, direst predictions and has come back to make a remarkable recovery. He has undergone four operations, remains partially paralyzed on his left side and regularly takes anti-seizure medication, but doctors at George Washington University Hospital said yesterday that he probably will go home to stay the day before Thanksgiving, returning to the hospital daily for physical therapy.

Doctors predict that if all goes well, Brady will be able to walk with a cane.

"I hope this room is always filled with as much integrity and good humor as Jim Brady has brought to it," Reagan said. "I'm proud that Jim Brady is my press secretary."

Nancy Reagan stood with her hand on Brady's shoulder. Brady's wife, Sarah; mother, Dorothy, and mother-in-law, Frances Kemp, looked on with pride as the president and Brady cut a red-white-and-blue ribbon to ceremonially open the renovated press room. "Nice job," Brady told the president as the ribbon fell away.

Reagan explained he had been practicing for the ribbon-cutting all morning on presidential counselor Edwin Meese III's tie.

In farewell, the president shook Brady's hand and Nancy Reagan hugged and kissed him.

"Am I still your 'Y and H' ? " he asked Mrs. Reagan as she bent over him.

Before Reagan named Brady his press secretary, there was widespread curiosity why the president-elect was waiting so long to give the job to the man who had become popular with reporters during the campaign and while serving as chief spokesman for the Reagan transition.

One theory reported was that Mrs. Reagan insisted that portly, balding Brady was not handsome enough to represent the Reagan administration.

Out of that, Mrs. Reagan explained to the crowd, came "my Y and H," her nickname for Brady, whose generally used nickname is "the Bear." "Y and H" stand for "youngest and handsomest," an echo also of the campaign nickname Sen. Paul Laxalt (R-Nev.) gave to Reagan, "the oldest and wisest."

"He's still my youngest and handsomest," Mrs. Reagan said.

"Take care, Mr. President," Brady said as he watched his boss leave the podium.

Then, as an attendant pushed Brady's wheel chair from the room and reporters called out their good wishes, the press secretary had the final word:

"I'll come back."