Figures show a drop of around a third since 2003 and the rate of improvement in Glasgow has been better than across Scotland as a whole.
The figures from the Scottish Government show hundreds fewer deaths for both men and women in the city, from two of the big killer diseases.
In 2012 there were 1720 deaths in Glasgow from heart disease, which had fallen to 1101 by 2003. Stroke deaths had also dropped over the same period from 719 to 481, or 49%.
The drop is welcomed as good news by health bosses. The Scottish Government said it had been following an action plan to reduce fatalities.
Across the country heart disease deaths fell by almost a third also, from 14,162 to 10,736 in 2012. Strokes fell by more than a fifth across Scotland.
Health Secretary Alex Neil said the key to reducing the figure further was lifestyle choices and getting fitter.
He said: "These figures show that our strategy for tackling heart disease and stroke is delivering real results for patients.
"It is fantastic that NHS Scotland is continuing to make significant cuts in the number of deaths from heart disease and stroke.
"Our Heart Disease and Stroke Action Plan sets out a comprehensive programme for further reducing deaths at whatever age.
"The plan focuses not just on providing the best care in the acute setting, but in helping people's longer-term recovery in their own comm-unities. Future improve-ments will largely depend on people's lifestyles, eating better, being more active, stopping smoking and drinking sensibly.
"We are taking firm action in all these areas to support people to live healthier lives."
Heart attack figures were also released for the Greater Glasgow and Clyde health board area, showing a drop of 25% with 800 fewer heart attacks.
There was an increase in strokes in the last year of 68 but overall, between 2003 and 2012 there was a drop of 13%
NHSGGC director of public health Dr Linda de Caestecker said: "This latest report confirms that the work we are doing to improve health and the on-going advances in medical care within Greater Glasgow and Clyde are paying dividends and we very much welcome the fall in deaths from heart disease and stroke.
"This reduction in deaths has also been influenced by prevention through the adoption of healthier lifestyles.
"We have been working hard with our local authority partners and with primary care colleagues for many years to improve diets and increase physical activity but we need to see further action on the prevention front to continue to see reduced deaths from heart disease and stroke".