He identified the falling birth rate as a major factor in the decline of the Scottish population.
Deaths now exceed births and this is a major factor in explaining why Scotland’s population has declined
Last month figures from the 2001 census showed that Scotland’s population had fallen by 2% in the last 20 years.
Mr Randall’s report said that the Scottish population stood at 5,064,011 last year.
He said this made it the only part of the UK with a declining population – a trend which is expected to continue.
“There are indications that factors which have affected demographic change in Scotland for many decades may now be changing,” said Mr Randall.
“For example, net emigration from Scotland in recent years has been much lower than in the 1960s or even the 1980s.
“And a declining birth rate means that deaths now exceed births and this is a major factor in explaining why Scotland’s population has declined or increased less strongly than in other countries.”
He added that the Scottish population was getting older.
The report also revealed that the number of children north of the border has reached a new low.
Last year 52,527 births were registered – the lowest number since civil registration began in 1855.
The number of women over the age of 30 giving birth rose from 23% in 1981 to 48% in 2001.
More than 43% of children were born outside marriage.
The number of deaths in Scotland last year was also at the lowest level since 1855, falling from 57,797 in 2000 to 57,382 in 2001.
Cancer and heart disease were the two most common causes of death, although the number of fatalities from heart disease has fallen by almost 30% over the last decade.
Despite the falling death rate in Scotland, it is still among the highest in both Britain and the European Union.
The birth rate is close to the European average, but lower than any other part of the UK.
It is predicted that the average life expectancy of boys born in 2001 will be 73.4, while girls can expect to live until they are 78.8.
Mr Randall’s report also showed that the number of divorces fell to 10,631 in 2001 – the lowest number since 1982.
However, the number of marriages also fell, from 30,367 in 2000 to 30,058 last year.
The average age of people getting wed for the first time was 31 for men and 29 for women – both showing an increase of about four years in since 1991.
The General Register Office for Scotland is the Scottish Executive department responsible for the registration of births, marriages, deaths, divorces and adoptions.