Less than one-fifth of the population described themselves as both Scottish and British in the census question on national identity, which was asked for the first time in the 2011 survey.
It shows that 62.4% of the country's 5.3 million people identify themselves as "Scottish only", while 18.3% said they were "Scottish and British only".
The latest census results also reveal that the population is becoming more ethnically diverse. Results show 4% of people are from non-white minority ethnic groups - double the proportion recorded in 2001.
Meanwhile, 7% of people living in Scotland were born abroad, up three percentage points on 2001. By far the highest number were born in Poland, at 55,000 people - a change from 2001 when the highest number of people born abroad were from the Republic of Ireland.
Culture Secretary Fiona Hyslop said: "The census results reveal a fascinating picture of Scotland today. While our society is more multi-cultural than ever before, and our communities more ethnically and religiously diverse, people here also have a very strong sense of Scottish identity.
"While 62% of people feel Scottish only, a further 21% of the population share their Scottish connection with another identity - the highest claim to a resident national identity anywhere in the UK.
"It is especially welcome that, amongst those proud to claim a Scottish identity, are those who have chosen Scotland as their home and the census reflects in particular the increase in our Polish and Asian populations."
She added: "These figures show that Scotland is an attractive and dynamic nation and one where people from many different backgrounds, cultures and nationalities want to make a life for themselves and their families and celebrate their Scottish identity."
Scottish Liberal Democrat leader Willie Rennie MSP urged caution when it comes to interpreting the results ahead of next year's referendum on independence.
He said: "Next year's referendum is not and should not be a choice about identity. Figures from the Scottish Social Attitudes survey show that less than half of those who feel Scottish and not British support independence.
"These figures confirm a long-running trend that identity is not the key battle-ground in deciding Scotland's future. It's a false and dangerous logic from the nationalists which says that Scottish people have to back independence to be patriotic."
The proportion of married people also fell from 2001 figures, down from 50% to 45%.