The figures, collated by the National Gallery of Scotland, the Scottish National Gallery of Modern Art and the recently revamped Scottish National Portrait Gallery, mark a 25% rise on 2011. The results are partly due to the opening of the refurbished portrait gallery in December 2011, although the Scottish National Gallery and the Scottish National Gallery of Modern Art saw rises of 3.9% and 4.5% respectively.
Sir John Leighton, director-general of the National Galleries of Scotland, said: "Art and culture are becoming increasingly important for attracting visitors to Scotland and we are working with colleagues and partners around the country to make a significant contribution to the tourist economy."
The Scottish National Portrait Gallery attracted 327,980 visitors in 2012, its first full year of opening after the renovation, up 39% on the last full calendar year of figures in 2008 before it closed for the refurbishment.
The highest previous figure for all three sites was 1.56 million in 2006.