The star was formed just a couple of hundred million years after the Big Bang that brought the Universe into being, they believe.
Previous contenders for the title of oldest star are around 13.2 billion years old -- two objects described by European and US teams respectively in 2007 and 2013.
Stefan Keller at the Australian National University in the Australian capital, Canberra, said the Methuselah star is -- in cosmic terms -- relatively close to us.
It lies in our own galaxy, the Milky Way, at a distance of around 6,000 light years from Earth. The star catalogues list it by the number of SMSS J031300.36-670839.3.
"The telltale sign that the star is so ancient is the complete absence of any detectable level of iron in the spectrum of light emerging from the star," Keller said in an email exchange with AFP about the study.
The Big Bang gave rise to a Universe filled with hydrogen, helium, and a trace of lithium, he explained.
All the other elements that we see today were forged in stars, which are born in clouds of gas and dust bequeathed by supernovae -- huge stars that explode at the end of their life.
This endless recycling process has yielded an intriguing tool for astrophysicists.
One way of determining stellar age is iron, whose content in a star enriches with every successive birth.
Thus the lower the iron content in a star's light spectrum, the older it is.
"The iron level of the Universe increases with time as successive generations of stars form and die," said Keller.
"We can use the iron abundance of a star as a qualitative 'clock' telling us when the star was formed.
"In the case of the star we have announced, the amount of iron present is less than one millionth that of the Sun and a factor of at least 60 times less than any other known star. This indicates that our star is the most ancient yet found."
The star was discovered using the Australian National University's SkyMapper telescope, which is carrying out a five-year survey of the southern sky.
The progenitor of the star was material from a low-energy supernova, from a star whose mass was roughly 60 times that of the Sun, according to the paper, published in the journal Nature.
Previous sweeps of the sky have turned up four other stars with similar very low iron content, which suggests that these kind of supernovae played a vital role in creating stars, and then galaxies, in the early Universe, it said.