As the world of sports shut down around him, International Olympic Committee president Thomas Bach spent a month insisting that the Tokyo Games would go off on schedule. It was only last weekend, in the space of 48 hectic hours, that he says his thinking changed on the biggest decision of his tenure.

The scramble began Sunday, he said, with a realization that the spread of the novel coronavirus was actually accelerating. That touched off a string of urgent conference calls with sports entities around the planet, culminating...