Data describing the incidence of hypertension and diabetes among people with HIV in sub-Saharan Africa remain sparse. In this study, adults with HIV were enrolled from a public clinic in Moshi, Tanzania (September 2020—March 2021). At enrollment, a survey was administered to collect information on comorbidities and medication use. Each participant’s blood pressure and point-of-care glucose were measured. Baseline hypertension was defined by blood pressure ≥140/90 mmHg or self-reported hypertension at enrollment. Baseline diabetes was defined by self-reported diabetes or hyperglycemia (fasting glucose ≥126 mg/dl or random glucose ≥200 mg/dl) at enrollment. At 6-month follow-up, participants’ blood pressure and point-of-care glucose were again measured. Incident hypertension was defined by self-report of new hypertension diagnosis or blood pressure ≥140/90 mmHg at follow-up in a participant without baseline hypertension. Incident diabetes was defined as self-report of new diabetes diagnosis or measured hyperglycemia at follow-up in a participant without baseline diabetes. During the study period, 477 participants were enrolled, of whom 310 did not have baseline hypertension and 457 did not have baseline diabetes. At six-month follow-up, 51 participants (95% CI: 38, 67) had new-onset hypertension, corresponding to an incidence of 33 new cases of hypertension per 100 person-years. Participants with incident hypertension at 6-month follow-up were more likely to have a history of alcohol use (90.2% vs. 73.7%, OR = 3.18, 95% CI:1.32–9.62, p = 0.008) and were older (mean age = 46.5 vs. 42.3, p = 0.027). At six-month follow-up, 8 participants (95% CI: 3, 16) had new-onset diabetes, corresponding to an incidence of 3 new cases of diabetes per 100 person-years. In conclusion, the incidence of elevated blood pressure and diabetes among Tanzanians with HIV is higher than what has been reported in high-income settings.