Background: With at least 94 countries undergoing or exiting lockdowns for contact suppression to control the COVID-19 outbreak, sustainable and public health-driven exit strategies are required. Here we explore the impact of lockdown and exit strategies in Singapore for immediate planning. Methods: We use an agent-based model to examine the impacts of epidemic control over 480 days. A limited control baseline of case isolation and household member quarantining is used. We measure the impact of lockdown duration and start date on final infection attack sizes. We then apply a 3-month gradual exit strategy, immediately re-opening schools and easing workplace distancing measures, and compare this to long-term social distancing measures. Findings: At baseline, we estimated 815 400 total infections (21.6% of the population). Early lockdown at 5 weeks with no exit strategy averted 18 500 (2.27% of baseline averted), 21 300 (2.61%) and 22 400 (2.75%) infections for 6, 8 and 9-week lockdown durations. Using the exit strategy averted a corresponding 114 700, 121 700 and 126 000 total cases, representing 12.07–13.06% of the total epidemic size under baseline. This diminishes to 9 900–11 300 for a late 8-week start time. Long-term social distancing at 6 and 8-week durations are viable but less effective. Interpretation: Gradual release exit strategies are critical to maintain epidemic suppression under a new normal. We present final infection attack sizes assuming the ongoing importation of cases, which require preparation for a potential second epidemic wave due to ongoing epidemics elsewhere. Funding: Singapore Ministry of Health, Singapore Population Health Improvement Centre.