This is a randomized (the study medication is assigned by chance), double-blind (neither physician nor participant knows the identity of the assigned treatment), placebo (an inactive substance that is compared with a drug to test whether the drug has a real effect)-controlled, event-driven, multicenter study in patients who are hospitalized for a specific acute medical illness and have other risk factors for venous thromboembolism (VTE). The study is designed to evaluate rivaroxaban in the prevention of symptomatic VTE events and VTE-related deaths for a period of 45 days post-hospital discharge. The study will consist of a screening phase, a 45-day double-blind treatment phase, and a 30-day follow-up phase. Study drug will start at randomization (Day 1), and will continue until Day 45 (inclusive). A total of approximately 12000 patients will be randomly assigned to either rivaroxaban or placebo in a 1:1 ratio. The total duration for a patient who completes the study after randomization is expected to be 75 days.