(1) Background: Smoking cessation may be very difficult, even if smoking aggravates the prognosis of a disease, which has been shown to be the case for persons with rheumatoid arthritis (RA). In contrast, an association in patients with osteoarthritis (OA) is still disputed. The primary objective was to compare smokers diagnosed with RA and OA to controls, regarding smoking cessation rates after following the intensive ‘Gold Standard Program’ (GSP). Secondary objectives included the identification of significant prognostic factors for successful quitting. (2) Methods: In total, 24,652 patients were included in this prospective cohort study, after attending the national GSP for smoking cessation intervention 2006–2016, as registered in the Danish Smoking Cessation Database. Data were linked to the National Patient Register. Hereof, 227 patients (1%) were diagnosed with seropositive RA and 2899 (12%) with OA. Primary outcome was continuous abstinence six months after the planned quitting date. (3) Results: In total, 16,969 (69%) of the patients participated in the follow-up interviews. The adjusted odds ratios for successful quitting were similar to the control group for both RA (1.28, 95% CI: 0.90–1.80) and OA patients (0.92, 0.82–1.03). The outermost, strongest positive factor for successful quitting was compliance, defined as attending ≥75% of the meetings. To a lesser degree, attending an individual intervention was a positive predictor, while being heavy smokers, disadvantaged smokers, women, living with a smoker, and if GSP was recommended by health professionals were negative predictors. (4) Conclusions: The odds ratios for quitting were similar to controls for both RA and OR patients. Additional research is needed to determine effective actions towards increased attendance at the programs.