A combination of more women waiting longer to have children and uncertainty over the economy are believed to be behind the slowdown.
There were 12,580 births in Scotland in the final three months of last year, according to figures released by National Records of Scotland (NRS).
Paul Lowe, the Registrar General for Scotland, said: “Continuing the downward trend since 2008, the number of births for the fourth quarter of 2018 has been at its lowest number recorded since civil registration began.
The total number of quarter four births fell to a previous low of 12,785 in 2000. It then rose to 14,540 in 2008 before falling in more recent years.
Ther were 14,484 deaths registered between October and december last year which was 4.7 per cent lower than in the same period of 2017 which marked a recent peak.
The number of cancer deaths fell by 1.6 per cent to 4,264, while deaths from heart disease fell by 5.4 per cent to 1,675.