Coughing in the morning can be very common in smokers due to the accumulation of toxins in the lungs, that your body then tries to cough out each morning. All of the toxins that you take in when you are smoking, in addition to causing cancer, raising your blood pressure, and ruining your teeth, also stun or kill your cilia and cause cell changes in the airway. Cilia are the small cells with microscopic brushes or fans on the edges of them, and their job is to sweep toxins and mucous out of the airway and to a point where you can cough them up. Now that you have stopped smoking (and killing them!), they are starting to work again to clean out your lungs. When you wake in the morning, you have all of the junk that was cleaned out overnight waiting to be coughed up.
Despite that possible explanation, anyone with a long smoking history and a chronic cough should be seen by their doctor
and probably have an x-ray
to make sure that there is nothing concerning, such as lung cancer-causing the cough. Congratulations on quitting smoking, now keep taking care of yourself by seeing a physician soon to discuss your cough.