There were 138 deaths in 2013 across the NHS Greater Glasgow and Clyde (NHSGGC) area, 49 fewer than the previous year.
In the Glasgow City Council area, the number of drug-related deaths fell from 121 to 103.
A spokeswoman for NHSGGC said: "The impact of drug misuse in some of our most deprived communities has enormous consequences for the people who take drugs, their families and the local community.
"NHS Greater Glasgow and Clyde offers a wide range of services to help people combat drug problems, including counselling, prescribed treatment, rehabilitation programmes, harm reduction services and relapse prevention."
NHS Ayrshire and Arran also reported a fall in drug- related deaths, from 43 in 2012 to 36 in 2013.
However, NHS Lanarkshire saw figures rise from 67 in 2012 to 75 last year.
The increase was in South Lanarkshire, where there were 37 drug-related deaths in 2013, compared to 29 in the previous year.
In North Lanarkshire the number of deaths was 38 in both 2012 and 2013.
There were 526 drug-related deaths across Scotland, down 9% on the 2012 figure of 581.
Just over 9 out of 10 deaths were of people who took more than one drug, with the majority of the deaths linked to heroin and methadone use.
In Greater Glasgow and Clyde, 53 deaths were linked to heroin and 51 were linked to methadone. Cocaine was a factor in the deaths of 17 people.
Despite an overall fall in the number of drug-related deaths, the number where New Psychoactive Substances (NPS), or legal highs, were present, rose from 47 in 2012 to 113 last year.
Director of the Scottish Drugs Forum, David Liddell, said: "These deaths, although reported separately, have more in common with Scotland's more familiar drug overdose deaths involving opiates, benzodiazepines and/or alcohol. So while the NPS element may be new, sadly the types of death are all too familiar."