The Association of Scottish Visitor Attractions (ASVA) said the figures showed a rise of over 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 1,234,557 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 special exhibition ever, attracting more than 123,000 visitors in its 23-week run.
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, which were backed by an award-winning marketing campaign, boosted numbers by almost 20%, while at Iona Abbey, which celebrated the 1,450-year anniversary of St Columba establishing the ancient holy site, visitor figures leapt by 1,178%.
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.
Inveraray Castle and Jail collectively saw a rise of 13%, attributed in part to the "Downton Abbey effect", with the castle featuring as Duneagle in the popular drama series.
Last year's good weather is also said to have benefited seaside destinations such as St Andrews, where the town's four major attractions recorded a rise of 9%.
The Highlands also fared well, with visitor numbers to Glencoe, location of some of the most dramatic scenes in the Bond movie Skyfall, up by over 37%.
The early season low temperatures, combined with snow at altitude, benefited the ski areas at CairnGorm Mountain and Nevis Range too, which saw figures rise by 9.5% and 8% respectively.
David O'Neill, chair of ASVA said: "Looking forward, we are confident that 2014 will be a bumper year for the visitor attractions sector in Scotland as we reap the benefits from Homecoming 2014 and major events including the Commonwealth Games and Ryder Cup, as well as the opening of exciting new attractions such as the Bannockburn Visitor Centre."