BOSTON — Senator Kennedy gave a thumbs up to well-wishers and kisses to relatives as he walked out of the hospital today, a day after learning he has a cancerous brain tumor.

A square bandage at the back of his head marked the spot where doctors performed a biopsy Monday that led them to diagnose the Massachusetts Democrat with malignant glioma. Experts say such tumors are almost always fatal.

Mr. Kennedy’s dogs, Sunny and Splash, met him at the hospital door. Hospital workers and well-wishers greeted Mr. Kennedy with applause. Before he and his wife, Vicki, got into a dark Chevrolet Suburban, he kissed his daughter, Kara, and his niece Caroline Kennedy, and embraced his son, Rep. Patrick Kennedy, a Democrat of Rhode Island.

The senator departed with a wave as television news helicopters followed his 75-mile trip south to his Cape Cod home. Along the way, he could be seen waving to nearby motorists from the front passenger seat of his SUV. He took a walk on the beach with his two Portuguese Water Dogs as soon as he arrived.

“Good to be back home,” he told waiting reporters before heading off for a sail on his sloop, “Mya.”

Doctors announced Mr. Kennedy “has recovered remarkably quickly” from the brain biopsy. They said he will recuperate at his home over the Memorial Day weekend while awaiting further test results that will help determine his treatment plan.

“He’s feeling well and eager to get started,” a top neurologist at Massachusetts General, Dr. Lee Schwamm, and Mr. Kennedy’s primary care physician, Dr. Larry Ronan, said.

The 76-year-old senator, the last son in a famed political family, was diagnosed with a malignant glioma in his left parietal lobe — which helps govern sensation, movement, and language — after suffering a seizure in his home Saturday morning. Malignant gliomas are diagnosed in about 9,000 Americans a year.

“It’s treatable but not curable. You can put it into remission for a while but it’s not a curable tumor,” a neuroncologist at Beth Israel Deaconess Medical Center in Boston, Dr. Suriya Jeyapalan, said.

In an e-mail yesterday, Vicki Kennedy told friends the grim diagnosis was “a real curveball” that left the family stunned even as Mr. Kennedy joked and laughed with them. She expressed pride in how her husband was handling the news.

“Teddy is leading us all, as usual, with his calm approach to getting the best information possible,” she wrote in an e-mail yesterday to friends.

“He’s also making me crazy (and making me laugh) by pushing to race in the Figawi this weekend,” she wrote, referring to the annual sailing race from Cape Cod to Nantucket.

The diagnosis cast a pall over Capitol Hill, where the Massachusetts Democrat has served since 1962.

Senator Byrd, a Democrat of West Virginia, the longest-serving member of the Senate, wept as he prayed for “my dear, dear friend, dear friend, Ted Kennedy” during a speech on the Senate floor.

“Keep Ted here for us and for America,” the 90-year-old Mr. Byrd, who is in a wheelchair, said. He added: “Ted, Ted, my dear friend, I love you and I miss you.”

In a statement, President Bush saluted Mr. Kennedy as “a man of tremendous courage, remarkable strength and powerful spirit.” He added: “We join our fellow Americans in praying for his full recovery.”

Mr. Kennedy has been active for his age, maintaining an aggressive schedule on Capitol Hill and across Massachusetts. He has made several campaign appearances for Senator Obama.

“He fights for what he thinks is right. And we want to make sure that he’s fighting this illness,” Mr. Obama said yesterday. “And it’s our job now to support him in the way that he has supported us for so many years.”

Senator Clinton said: “Ted Kennedy’s courage and resolve are unmatched, and they have made him one of the greatest legislators in Senate history. Our thoughts are with him and Vicki and we are praying for a quick and full recovery.”

Mr. Kennedy has left his stamp on a raft of health care, pension, and immigration legislation during four decades in the Senate. In 1980, Mr. Kennedy unsuccessfully challenged Jimmy Carter for the Democratic presidential nomination.

The Kennedy family has been struck by tragedy over and over. Mr. Kennedy’s eldest brother, Joseph, died in a World War II plane crash; President Kennedy was assassinated in 1963; and Senator Robert F. Kennedy was assassinated in 1968.

Ted Kennedy shocked the nation in 1969 when he drove his car off a bridge to Massachusetts’ Chappaquiddick Island and a young female campaign worker drowned. Mr. Kennedy, who did not call authorities until the next day, pleaded guilty to leaving the scene of an accident and received a suspended two-month jail sentence.

Mr. Kennedy, the Senate’s second-longest serving member, was re-elected in 2006 and is not up for election again until 2012. Were he to resign or die in office, state law requires a special election for the seat 145 to 160 days afterward.