The smokers will each get a £12.50 electronic credit to spend at Asda per week they don't smoke and will be breath-tested at local pharmacies to ensure they have not succumbed.
The quit4u scheme was launched this month and will run for two years before the Scottish Parliament decides whether to offer it across the country. A spokeswoman for NHS Tayside, Dundee's local health authority, said the plan was "to roll it out" across Scotland.
There are 36,000 smokers in disadvantaged areas in Dundee, according to NHS Tayside, and it is hoped 1,800 people will be recruited and up to half will give up smoking.
"The most important thing anyone can do to improve their health is to quit smoking - it's the biggest preventable cause of ill-health and premature death in Scotland," said Shona Robison, Scottish minister for public health and sport. "This is an innovative project and I'll be following the results to see if there are lessons for the rest of Scotland."
One of the first participants is 47-year-old Valerie Cowan of Dundee who has smoked 20-30 cigarettes a day for the past 30 years. The scheme will cost £550,000 over the two-year period, with an average of £1,300 per person being spent. "Smoking rates are very closely aligned with poverty," said deputy director of public health, Paul Ballard. "We believe that by offering this incentive we will be helping to deliver a change in the health of those who need it most."
Eligibility is limited to those living in areas classed as "disadvantaged" - ie, with the highest levels of unemployment in the city. Once a person has been accepted on the scheme, they will need to make weekly visits to their local pharmacy where they will breathe into a carbon monoxide testing machine.
Smoke-free participants will get a credit for a maximum of 12 weeks.