Globular clusters like M4 contain the Mily Way's oldest stars
It puts this at between 13 and 14 billion years old - consistent with recent estimates by cosmologists based on other evidence.
International astronomers used the Hubble to hunt for very small burnt-out stars in our galaxy, known as white dwarfs.
These objects were found among a giant group of ancient stars - the globular cluster M4 - some 7,000 light-years away.
The stars are still giving off heat, which can be measured by the orbiting space telescope.
The cooling cinders give an indication of when the white dwarf stars were born - just under 13 billion years ago.
The first stars are thought to have formed about a billion years after the Big Bang, suggesting the Universe is 13-14 billion years old.
This is consistent with calculations by cosmologists based on measurements of how fast the Universe is expanding.
'Real triumph'
The results were announced at a press conference of the US space agency (Nasa) in Washington DC.
Scientists said the age they came up with - just under 14 billion years give or take 500 million years or so - was calculated using a different method from earlier estimates.
It offers independent verification that astronomers were on the right track, they told reporters.
"It's almost as if we were saying, 'you always thought you knew how old you were, but you never had proof'," said Bruce Margon of the Space Telescope Science Institute.
"One day, you open a drawer and there's your birth certificate, and you get the same answer. That's a real triumph."
A 12-member international team carried out the research. The study has been submitted for publication to The Astrophysical Journal Letters.