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.
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.
"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.