A report by Oxford University's Migration Observatory found Scotland's foreign-born population rose from 191,571 to 369,284 - an increase of 93% - between 2001 and 2011.
The rise was much bigger than in other parts of the UK, where the number of immigrants living in England increased by 61%, in Wales by 82% and in Northern Ireland by 72%.
However, at just 7% the proportion of foreign-born residents in Scotland is still considerably smaller than the 13% south of the Border.
The Scottish Government has welcomed the findings, claiming they support its plan to increase immigration if Scotland becomes independent to help boost the economy and support a rapidly ageing population.
The Migration Observatory research body found the sharp rise in Scotland's migrant population was fuelled by a huge rise in the number of Polish-born residents, who acquired the right to live and work anywhere in the EU in 2004.
The population grew from 2505 in 2001 to 55,231 in 2011, making Polish people the country's largest immigrant group.
People born in India (23,489 at the last census count in 2011, more than double the 2001 figure) and Ireland (22,952, up 5%) made up the second and third largest immigrant groups.
Other significant national groups included people born in Pakistan, Germany, the USA and China.
The second-fastest growing immigrant group, after Poles, was Nigerians, whose numbers leaped from 1253 to 9458.
Lead researcher Dr Carlos Vargas-Silva said: "This is the last census before the referendum on independence, and population is an important part of the discussion.
"While Scotland still has a much smaller foreign-born population than England, it has almost doubled in a decade. But as Scotland started with a much smaller migrant population than England, both numerically and in terms of its share of the overall population, smaller numerical growth can be considerably bigger growth in percentage terms.
"Nevertheless, there has been a large increase in the migrant population of Scotland, especially in Aberdeen, Glasgow and Edinburgh."
Nearly two-thirds of Scotland's present immigrant population moved to the country after 2001, the analysis found.
Edinburgh is home to the highest number in any single council area, at 75,696 residents, or 15.8% of the capital's total population.
In Aberdeen, the place with the fastest rising immigrant population in Scotland, numbers rose from 13,264 to 35,436 over the 10-year period. Foreign-born residents now make up 15.9% of the city's population, the highest proportion in the country.
Glasgow's overseas-born residents rose from 32,690 to 72,607, or 12% of the city's population.
The smallest proportion of immigrants was in East Ayrshire, whose 2774 foreign-born residents amounted to 2% of the total population.
First Minister Alex Salmond has put plans to encourage further immigration at the heart of his case for independence, as outlined in the government's White Paper blueprint last week.
It proposes an Australian-style points system allowing people with skills needed in the economy to qualify to settle in Scotland more easily. Overseas students would also be encouraged to stay and work in Scotland after completing their studies.
Welcoming the new analysis, a Scottish Government spokeswoman said: "As we said when we published Scotland's Future last week, Scotland has very different demographic and migration needs to the rest of the UK.
"The current immigration system has not supported Scotland's migration priorities."
A poll at the weekend found only 21% of voters believed more immigration would boost the economy. Scots Tory MSP John Lamont warned border controls were "a real possibility" if an independent Scotland adopted a different immigration policy from the rest of the UK.