Background The optimal medical strategy for prevention of thromboembolic events after surgical bioprosthetic aortic valve replacement (BAVR) is still debated. The objective of this study was to compare warfarin therapy (target INR of 2.0 to 3.0) with aspirin 150 mg daily as antithrombotic therapy for the first three months after BAVR with or without concomitant coronary artery bypass grafting (CABG). The aim was to evaluate thromboembolic complications, major bleeding complications and death. Materials and methods Prospective, single-centre, open-label, randomized controlled trial. 370 patients were enrolled, 328 were available for data analysis. Results At baseline the warfarin and aspirin groups were comparable. Thromboembolic events were comparable between groups 11 (6.6%) vs. 12 (7.5%), p = 0.83. Major bleeding events occurred numerically more often in warfarin patients 9 (5.4%) vs. 3 (1.9%), p = 0.14. Warfarin was in multivariate analysis significantly associated with major bleeding OR 5.18 (CI 1.06–25.43), p = 0.043. 90-day mortality was comparable between groups 8 (4.7%) vs. 6 (3.7%), p = 0.79. Conclusions Our results suggest that aspirin might be equally effective as warfarin in preventing thromboembolic events after BAVR, but with less major bleedings. Although this is numerically the largest trial testing this hypothesis in a prospective randomized trial, further adequately powered studies are warranted.