Background: Delirium is a common neuropsychiatric syndrome in hospitalized elderly patients and is associated with poor clinical outcomes. We aimed to determine the prevalence, recognition, risk factors, and course of delirium among hospitalized elderly (65 years of age or older) patients at Sultan Qaboos University Hospital (SQUH). Methods: A prospective cohort study included 327 elderly patients (65 years of age or older) admitted to the medical wards at SQUH. Patients were screened for delirium using the 3-Minute Diagnostic Confusion Assessment Method (3D-CAM). Additionally, medical records were reviewed to identify possible associated factors. Results: The prevalence of delirium was 55.4% (95% CI 49.9–60.7), and 35.4% of patients with delirium were not recognized by the treating team. Hypoactive delirium is the most common type of delirium. The logistic regression analyzes demonstrated that pre-existing cognitive impairment (OR = 4.0); poor functional status (OR = 1.9); the use of medications that are known to precipitate delirium (OR = 2.3); polypharmacy (OR = 5.7); urinary catheterization (OR = 2.2); dehydration (OR = 3.1); and electrolytes derangements (OR = 2.0) were independent risk factors for delirium. Furthermore, 56.9% of patients with delirium continued to have delirium upon discharge from the hospital. Conclusions: Delirium is common among elderly patients hospitalized in general medical wards. Implementing effective preventive strategies for delirium during the hospital stay, including early recognition using standard sensitive and specific screening tools (i.e., 3D-CAM) and developing geriatric wards, is crucial.