The dramatic reversal of fortunes will be revealed this week in a report by the General Registers of Scotland, which also records that births have exceeded deaths for the first time in a decade.

The biggest factor has been inward migration from other parts of the UK and other, mainly eastern European, countries.

Immigrants from nations such as Poland have also had a significant effect on the birth rate, with one in three of the babies born in Scotland last year having foreign parents.

The new statistics, to be published by the General Registers of Scotland, mark a remarkable turnaround from four years ago when the then First Minister, Jack McConnell, claimed that Scotland was sitting on a "demographic timebomb". He warned that the population was in real danger of slipping below five million by 2009 and branded it the "biggest single threat" facing the country.

McConnell's 'Fresh Talent' initiative, aimed at attracting skilled migrants to Scotland, is believed to be one of the factors behind the reversal.

The SNP has continued to welcome immigrants since coming to power.

The latest increases in immigration and birth rates means that Scotland's population is now projected to stay above five million until the 2070s.

The Registrar General's figures will reveal that, since 2003, Scotland's population has increased from 5.06 million to 5.14 million. The total, for mid-2007, represents a 27,300 rise on the previous year and is the highest figure since 1983.

Last year, for example, 63,000 Scots residents left the country but there were almost 90,000 new arrivals. They included a net gain of 8,800 people from the rest of the UK, 16,800 from overseas and 1,200 members of the armed forces.

2007 was also the fifth consecutive year that the number of births had risen but the only one in which births totalled more than deaths.

Business leaders welcomed the figures. Liz Cameron, director of the Scottish Chambers of Commerce, said they were "a further sign of renewed vitality in Scotland's population".

"The change in the last four years has clearly been net in-migration from new accession states of the EU. This probably peaked at the time of the survey and the challenge now is to encourage these very welcome workers to stay and make a new life in Scotland."

Stuart Mackinnon, spokesman for the Federation of Small Businesses Scotland, added: "A larger population and a larger working population for Scotland is very good news for small businesses. However, our understanding is that immigration from Eastern Europe is now starting to move back in the other direction. It is important to convince skilled labourers from abroad and the talented people that Scotland produces to actually remain in Scotland."

The latest statistics counter previous forecasts that Scotland was facing a damaging population decline. The Westminster Government Actuary had predicted that Scotland's population would fall below five million by next year, based on the fact that the nation's population had been falling for two decades and that no other part of the UK had a lower birth rate.

If that forecast had proved accurate, the population decline could have had a severe effect on the economy, leaving too few people of working age in Scotland to meet the needs of employers and to raise enough taxes to pay for soaring numbers of pensioners.

The influx of migrants from Eastern Europe, especially Poland, began in 2004 when they became eligible to work in the UK after their countries joined the EU. Home Office figures indicate that more than 52,000 citizens from the former communist states have registered to work in Scotland.

Around one third of the babies born in Scotland last year were to mothers born in Eastern Europe, and earlier this year the Scottish Government revealed that there are 3,347 school pupils whose first language is Polish.

The figures appear to vindicate the previous Scottish Executive's decision in 2004 to launch the Fresh Talent initiative, a drive to encourage 8,000 more skilled workers to put down roots in Scotland.

McConnell launched a website, scotlandistheplace.com, which was designed to sell the virtues of the country to potential migrants. The SNP Government has continued the scheme. Finance and Sustainable Growth Secretary John Swinney said there were clear dangers if Scotland's population growth continued to lag behind the UK.

Earlier this year, he said: "An increasing population has the potential to boost Scotland's economic growth. Without increasing labour participation among older people or attracting more people of working age to Scotland, adverse economic impacts are likely." A report by the Registrar General on demographic change forecast earlier this year that, based on past trends, the greatest areas of population growth would be Perth and Kinross (28%), West Lothian (22%), East Lothian (21%), Aberdeenshire (19%), Edinburgh (17%), Borders (15%) and the Orkney Islands (14%).

Overall in Scotland, it predicted the number of households would increase due to more people living alone.