Background Happiness and achievement motivation are two important concepts in students' lives. Therefore, this study was aimed at investigating the association between happiness and achievement motivation in undergraduate nursing students and examining their relationship with students' demographic characteristics. Method A descriptive correlational study was undertaken; 255 undergraduate nursing students enrolled in one nursing school in an urban area of Iran during the academic year 2017-2018 were included in the study using census method sampling. The demographic data questionnaire, Oxford Happiness Questionnaire (OHQ), and Hermans Achievement Motivation Questionnaire (HAMQ) were used for data collection. Data were analyzed using univariate analysis and multivariate linear regression analysis. Results The total mean (SD) of happiness and achievement motivation scores were 40.73 (11.20) and 82.61 (7.50), respectively. There was a direct significant correlation between happiness and achievement motivation (r = 0.36, p < 0.001). An inverse significant association between happiness and students 21-24 years old (β = −3.99, p < 0.03) was found. There was a direct significant association between happiness and being married (β = 5.33, p = 0.03) and interest in nursing (β = 4.78, p = 0.02). Additionally, achievement motivation was associated directly with female gender (β = 1.93, p = 0.03) and interest in nursing (β = 3.71, p = 0.005) and inversely associated with studying in the fourth academic year (β = −3.06, p = 0.03) and history of course drops (β = −3.45, p = 0.002). Conclusion Our study indicated that there was a direct significant relationship between happiness and achievement motivation in undergraduate nursing students. Therefore, officials and nursing education lecturers should consider programs to increase students' happiness, such as counseling or emotional support programs and workshops.