There were 584 such deaths in 2011 - the highest total ever recorded and 20% more than the previous year's figure of 485.
According to the figures, one in every hundred deaths last year was linked to drugs.
The statistics, published by the Registrar General, also showed a big rise in the number of deaths where the heroin substitute methadone had been taken.
The drug, which can be prescribed to addicts to help them kick their habit, was involved in 275 deaths last year - up from 174 in 2010.
The number of deaths involving heroin and/or morphine fell over the same period, going from 254 in 2010 to 206 last year.
Methadone potentially contributed to 47% of all drugs deaths while heroin and/or morphine was implicated in 35%.
Meanwhile, benzodiazepines, such as diazepam, potentially contributed to 185 deaths - 32% of all drug-related fatalities.
Cocaine, amphetamines and ecstasy were involved in 36, 24 and eight deaths respectively.
Community safety minister Roseanna Cunningham said every drugs-related death was a "tragedy" as she pledged the Scottish Government would continue work to tackle the problem.
She added: "Scotland has a legacy of drug misuse that stretches back decades, creating this upward ten-year trend in drug-related deaths.
"Many of those lost to us are older drug users who, after years, have become increasingly unwell.
"No Government has done more to address the legacy and while it will take time to tackle this tragedy, we will do that through continuing to invest and support the recovery of those affected by drugs in Scotland."
The overall number of drugs deaths has risen in six out of the last ten years, with the total for 2011 76% more than a decade ago, with 332 drug-related deaths in 2001.
Almost three-quarters of those who died last year were men - with 429 male fatalities compared to 155 women.
The largest number of those who died were between 35 and 44 years old, with 212 deaths in this age group.
Meanwhile 58 of those who died were under 25, 184 were aged between 25 and 34, 94 were between 45 and 54 and just 36 were older than 55.
The three health board areas which saw the largest number of drugs death were Greater Glasgow and Clyde with 192, Lothian with 73 and Grampian with 58.
Ms Cunningham said: "These figures published today represent 584 lives lost in communities across Scotland.
"Every one of these deaths is a tragedy and I extend my sympathies to the family members, friends and everyone connected."
But she stressed: "It is this Government's firm belief that recovery from serious drug addiction is possible."
She highlighted Government action aimed at tackling the problem, with £28.6 million being invested in frontline drug treatment and recovery services in 2012-13 - over 20% more than in 2006-07.
Ms Cunningham said waiting times for treatment were down "dramatically", with the Government on course to achieve a maximum wait of three weeks by 2013.
She went on: "We are achieving our commitment to offer long-term supported recovery to all who need it - a commitment which has seen 15,000 people coming in to treatment in 2011-12, bringing the total to more than 40,000 since 2007."
The minister insisted Scotland was "leading the way in recovery and developing innovative ways of supporting hard-to-reach groups in to recovery".
She vowed: "We will continue to work closely with the independent group of experts National Forum for Drug Related Deaths and partners from the voluntary, statutory, policy and academic fields to tackle the number of drug-related deaths.
"No-one is lost to us - people can and do recover from drug problems and addiction."
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