Experts told the Associated Press news agency that the type of tumour Kennedy is suffering from is almost always fatal.
However, doctors said Kennedy had recovered "remarkably quickly" following his brain biopsy and that he was "feeling well and eager to get started".
He was airlifted from his home in Cape Cod, Massachusetts, to the Boston hospital on Saturday after falling ill.
Kennedy is to recuperate at his home for the next few days while doctors await further test results and determine his treatment plan, AP reported.
Kennedy's diagnosis comes six months after he had surgery to clear a blockage in a major neck artery, a common procedure to prevent a stroke.
Bush's praise
On Tuesday George Bush, the US president, released a statement on Tuesday praising Kennedy as a man of "tremendous courage, remarkable strength, and powerful spirit".
He said he and his wife Laura's thoughts "are with Senator Kennedy and his family during this difficult period".
First elected to the US senate in 1962, Kennedy is the second longest-serving senator after Robert Byrd of West Virginia.
He ran for the Democratic presidential nomination in 1980, but lost the race to Jimmy Carter, the incumbent president.
Family dynasty
Edward Kennedy is only surviving brother of John F Kennedy, the US president who was assassinated on November 22, 1963 in Dallas, Texas,
His brother Robert Kennedy was also assassinated in 1968, shortly after he announced his bid for the US presidency.
The eldest brother, Joseph Patrick Kennedy, was killed in World War II.
Edward Kennedy is a well-known supporter of liberal causes and recently endorsed Barack Obama, the Democratic presidential hopeful.
Al Jazeera's Rosalind Jordan described Kennedy as a "liberal lion ... someone who has always stood up for the interests of working people and the poor".
Chappaquiddick incident
In 1969, after he accidentally drove his car off a bridge as he headed to Massachusetts' Chappaquiddick Island, a young female campaign worker he was with drowned.
Kennedy, who did not call authorities until the next day, pleaded
guilty to leaving the scene of the accident and received a suspended two-month jail sentence.
The incident is thought to have cost him the chance of running for the US presidency.