A delivery system and method for delivering a prosthetic heart valve to the aortic valve annulus via a transaortic approach. The system includes a balloon catheter for delivering a balloon-expandable prosthetic heart valve through an introducer from an approach from outside the patient, through a minimally-invasive opening in the chest cavity through an incision in the aorta, and into the aorta and aortic annulus. The balloon catheter includes a flexible, tapered tip just distal of the balloon to facilitate positioning of the prosthetic heart valve in the proper orientation within the aortic annulus. The prosthetic heart valve may be installed over the existing calcified leaflets, and a pre-dilation valvuloplasty procedure may also be utilized.