The Association of Scottish Visitor Attractions said the figures showed a rise of more than 225,000 (0.6%) on 2012's numbers.
The 2013 Visitor Trends Report analysed more than 250 of the organisation's member sites. Sectors which fared particularly well include heritage properties, sports and outdoor activity venues and distilleries.
For the third year, the National Museum of Scotland was the most visited attraction with 1,768,090 visits recorded. Edinburgh Castle was the highest paid entry attraction with 1,420,027 visits.
Edinburgh continued to dominate the marketplace, with 11 of the top 20 attractions located in the city. However sites in the north and south of Scotland recorded the biggest increases in numbers, with visits up by over 7% in both regions.
Whisky tourism continued to draw visitors to Scotland, with the majority of whisky-based attractions reporting a rise in their numbers. The Scotch Whisky Experience in Edinburgh experienced its highest ever visitor numbers, 11.5% up on the previous year.
The Jack Vettriano retrospective at Kelvingrove Art Gallery and Museum was the attraction's most successful exhibition ever, bringing in more than 123,000 visitors.
The Brick City exhibition at Paisley Museum, a display of the world's most iconic buildings and landmarks by Lego artist Warren Elsmore, was so successful that it was extended by two weeks to meet demand, helping to boost visitor figures by almost 70% for the year.
Two jousting weekends at Linlithgow Palace, boosted numbers by almost 20%, while at Iona Abbey, visitor figures leapt by 6%.
Edinburgh Zoo bucked the trend of other giant panda zoos the year after their pair arrived, recording only a small 6% decrease in 2013, with visitor numbers still remaining 40% higher than "pre-panda" figures.