The trio were honoured for the discovery of how chromosomes are protected by telomeres and the role of an enzyme called telomerase in maintaining or stripping away this vital shield.
"The award of the Nobel Prize recognises the discovery of a fundamental mechanism in the cell, a discovery that has stimulated the development of new therapeutic strategies," the Nobel jury said. Previous US winners of the same award.
The three told Swedish Radio they were overjoyed by the news.
Greider said she was "just thrilled, I just think that the recognition for curiosity-driven basic science is very, very nice," adding that she was up doing laundry in the US when the early morning call came from Sweden.
Blackburn said she knew when they made their discovery that they were on to something big.
"I felt very excited ... and I thought this is very interesting, this is a very important result, and you don't often feel that about a result," she said.
Szostak said meanwhile he expected "to have a big party at some point" to celebrate the prestigious award.
Telomeres are a minute yet vital factor in ageing. They are like a nubby, protective cap, fitting on the ends of the strands of DNA -- the chemical recipe for life -- that are packed into chromosomes.
Blackburn and Szostak discovered in 1982 that a unique DNA sequence in the telomeres protects the chromosomes from degradation when the cells divide. With Greider, Blackburn also identified telomerase, the enzyme that makes the telomere DNA.
If telomeres become worn, cells age.
But if telomerase levels are high, the telomere length is maintained, and cellular ageing is braked. A small number of rare but very destructive diseases, including a form of severe anaemia, are linked to defective telomerase, resulting in damaged cells.
Yet there is also a darker and more complex side to this picture.
Many experts initially speculated that ageing could be pinned to telomere shortening, but the process has emerged as something that encompasses different factors, as well as telomeres.
In addition, high telomerase also helps cancer, enabling its cells to replicate endlessly and achieve what scientists call "cellular immortality."
Finding ways of blocking this machinery through "telomerase inhibitors" is one of the most eagerly explored areas of cancer research.
The trio's work has "added a new dimension to our understanding of the cell, shed light on disease mechanisms, and stimulated the development of potential new therapies," the Nobel citation said.
The three won the 2006 Lasker Prize, one of the most prestigious US science awards, for the same work.
Blackburn has been a professor of biology and physiology at the University of California in San Francisco since 1990, while Greider is a professor in the department of molecular biology and genetics at Johns Hopkins University School of Medicine in Baltimore.
Szostak is professor of genetics at Massachusetts General Hospital in Boston and affiliated with the Howard Hughes Medical Institute.
Last year, the Nobel Medicine Prize went to France's Francoise Barre-Sinoussi and Luc Montagnier, who shared one half of the award, for discovering the human immunodeficiency virus (HIV) that causes AIDS. Recent winners of the Nobel Medicine Prize.
Harald zur Hausen of Germany won the other half for research that went against the then-current dogma to claim that a virus, the human papillomavirus (HPV), causes cervical cancer, the second most common cancer among women.
The Medicine Prize is the first award to be announced in this year's Nobel season.
The Physics Prize is to be announced on Tuesday followed by the Chemistry Prize on Wednesday. The Literature Prize will be announced on Thursday and the Peace Prize on Friday.
The Economics Prize will wrap up the awards on October 12.
The Nobel prizes, founded by Swedish industrialist Alfred Nobel, were first awarded in 1901.
Nobel, the inventor of dynamite, died childless in 1896, dedicating his vast fortune to create "prizes to those who, during the preceding year, shall have conferred the greatest benefit on mankind."
Laureates receive a gold medal, a diploma and 10 million Swedish kronor (1.42 million dollars, 980,000 euros) which can be split between up to three winners per prize. The prizes are awarded in Stockholm and Oslo on December 10.