Scotland still has a far higher rate than the rest of the UK, but health officials believe there is a "recent and sustained" decline.
Falling incomes among the poorest income groups is cited as one possible reason as alcohol becomes less affordable.
Health Secretary Alex Neil said it was proof that minimum pricing could save lives.
The report found that alcohol-related deaths among men in Scotland increased between 1991 and 2001 by 75% to 28 deaths per 100,000 people.
However there had been a fall from the peak year in 2003 of 30%.
For women the rate was 13.8 deaths per 100,000, up 56%, but also a fall from the peak year in 2006 of 19%.
In England and Wales for both sexes the rate was lower, but the overall increase higher and the recent decrease lower.
The report by NHS Health Scotland showed the amount of pure alcohol sold per person had reduced in the last three years but remain about 20% higher than in England and Wales.
There is still more alcohol drunk by "harmful drinkers" in the most deprived communities.
The study showed a fall in drinking between 2009 and 2011 with the economic downturn credited with making alcohol les affordable as incomes fell.
The report stated: "Scotland has a very high-level of alcohol-related harm.
"Although a number of key indicators of alcohol-related morbidity and mortality have begun to show falls in recent years, alcohol-related mortality rates in Scotland are approximately two times higher than they were in the early 1980s and remain nearly twice as high as those in England & Wales."