In 2016, the Netherlands was required to introduce new European Union (EU)’s (pictorial) tobacco health warnings. Our objective was to describe the pathways through which the new EU tobacco health warnings may influence quit attempts and smoking cessation among Dutch smokers. Longitudinal data from 2016 and 2017 from the International Tobacco Control (ITC) Netherlands Survey were used. Smokers who participated in both surveys were included ( N = 1017). Structural equation modeling was applied to examine the hypothesized pathways. Health warning salience was positively associated with more health worries (β = 0.301, p < 0.001) and a more positive attitude towards quitting (β = 0.180, p < 0.001), which, in turn, were associated with a stronger quit intention (health worries: β = 0.304, p < 0.001; attitude: β = 0.340, p < 0.001). Quit intention was a strong predictor of quit attempts (β = 0.336, p = 0.001). Health warning salience was also associated with stronger perceived social norms towards quitting (β = 0.166, p < 0.001), which directly predicted quit attempts (β = 0.141, p = 0.048). Quit attempts were positively associated with smoking cessation (β = 0.453, p = 0.043). Based on these findings, we posit that the effect of the EU’s tobacco health warnings on quit attempts and smoking cessation is mediated by increased health worries and a more positive attitude and perceived social norms towards quitting. Making tobacco health warnings more salient (e.g., by using plain packaging) may increase their potential to stimulate quitting among smokers.