The campaign, launched on Monday, will focus on the west of the city for four weeks, following the launch of a pilot scheme in the area aimed at making local level environmental improvements.
Recorded incidences of dog fouling are highest in west Belfast, but the Your Dog, Your Job campaign will later be rolled out across the city.
"Most of the complaints council receive are about dog fouling," SDLP councillor Pat McCarthy, chair of Belfast City Council's Health and Environmental Services Committee, said.
"People are fed up with it littering our streets and are frustrated that some dog owners still think it's okay not to clean up after their pet."
Our dog wardens will be out and about and if you're caught not cleaning up after your dog, you face an £80 fine.
Pat McCarthy, Belfast City Council
Speaking as a dog owner himself, Mr McCarthy added that there was simply no excuse for not cleaning up after pets.
"It's not about making this into a witch hunt, but we've tried the softly, softly approach of appealing to people's better nature and, quite frankly, it hasn't worked. We're not seeing the behavioural change that we'd like to," he said.
"Not only is it unsightly and inconvenient, there are also health risks associated with dog faeces which can be harmful to people - especially children.
"You don't need a special bag or a special bin - we all have plastic bags at home, so pop a couple in your pocket when you're out with the dog and there are hundreds of litter bins dotted around the city on streets or in parks and you can use any one of them."
Members of the public are also being encouraged to report repeat offenders to the council, giving as much information as possible to the dog wardens so they can try to take action.
Last year, 1,213 fines were issued in relation to dogs that had strayed. But 135 owners were also fined for not cleaning up while out and about with their pets.
Members of the public can report dog fouling in their area by calling Belfast City Council on 028 90 270431 or by emailing email@example.com.