Abdominal aortic aneurysms (AAA) are fatal in 80% of the cases when ruptured. Hypertension has been considered a potential risk factor for AAA; but the findings from prospective cohort studies have not been entirely consistent, nor have they been summarised in a comprehensive meta-analysis. Our aim was to conduct a systematic review and meta-analysis of cohort studies of the association between blood pressure, hypertension and AAA to clarify the strength and shape of these associations. We searched PubMed and Embase databases for relevant cohort studies up to April 30th, 2018. Random-effects models were used to calculate summary relative risks (RRs) and 95% confidence intervals (CIs). The meta-analysis included 21 cohort studies (20 publications) with data on 28,162 cases and 5,440,588 participants. The findings indicate that the RR of AAA in hypertensive patients is 1.66 times (95% CI: 1.49–1.85, I2 = 79.3%, n = 13) that of non-hypertensive patients. In addition, there was a 14% (95% CI: 6–23%, I2 = 30.5%, n = 6) and a 28% (95% CI: 12–46%, I2 = 80.1%, n = 6) increase in the RR of AAA for every 20 mmHg and 10 mmHg increase in systolic blood pressure (SBP) and diastolic blood pressure (DBP), respectively. The analysis of DBP showed evidence of a strong and highly significant nonlinear dose–response relationship (p < 0.001) with a steeper association from 80 mmHg and above. This meta-analysis suggests that hypertension increases the risk of developing AAA by 66%. Further studies are needed to clarify the underlying mechanism explaining the much stronger association between DBP and AAA than for SBP.