Scientists say they are adding the so-called leap second onto the end of December 31 by tweaking their atomic clocks, the world's most precise timekeepers, so they stay synchronised with the Earth's rotation.
That means Saturday night's countdown will be 5, 4, 3, 2, 1 - and 1.
Leap seconds are added because atomic clocks tend to run slightly ahead of the Earth's rotation, largely because of the friction of tides raised by the sun and moon.
It will be the first extra second added in seven years, Britain's Royal Astronomical Society said.
Both civilian and military users have come to depend on the ultra-precise time generated by atomic clocks.
The US Defence Department's master clock is required to be accurate to less than a billionth of a second per day.
The decision to lengthen 2005 was made by the International Earth Rotation and Reference Systems Service based at the Paris Observatory in France.
The practice of adding seconds to selected years began in 1972.
But more seconds may have to be added more rapidly in years to come if Earth, as predicted, slows down its rotation "on a nearly exponential scale", according to Geoff Chester, a spokesperson for the US National Institute of Standards and Technology - the observatory that keeps official US time.
Dr Chester, who was quoted by the National Geographic magazine online, said the slowdown is expected to come from the rising tidal friction.