On the morning of Sunday, April 8, Facebook Inc.'s youthful chief executive, Mark Zuckerberg, alerted his board of directors that he intended to buy Instagram, the hot photo-sharing service.

It was the first the board heard of what, later that day, would become Facebook's largest acquisition ever, according to several people familiar with the matter. Mr. Zuckerberg and his counterpart at Instagram, Kevin Systrom, had already been talking over the deal for three days, these people said.

Negotiating...