Mr. O’Brien’s deep pockets  his company, Digicel, dominates the Haitian cellphone market and he himself is worth an estimated $3.5 billion  allowed him to hire hundreds of workers, import materials and not flinch too much at cost overruns. He flew in every few weeks for site visits, and constantly hounded his project manager, George Howard, for updates and photographs.

“When you go down that main street there, and see tens of thousands of people milling about the place, with barely an umbrella; these people, they’re just incredible, selling every day to make a livelihood,” Mr. O’Brien said a few days before the inauguration, scheduled for Tuesday. “Every day that we delay, it’s just more misery for the people outside the gate.”

He is also keenly aware of the financial upside to getting Haiti up and running again. “As a company, we’re more aligned to the masses than to the elites,” Mr. O’Brien said of his interest in the market.

Like so much of Haiti’s architectural heritage, the Iron Market was in bad shape long before the earthquake. It had suffered for decades from lack of maintenance, and in May 2008, a fire devastated the north hall. A year and a half later, that section was still a jumble of detritus, barely shielded from scavengers by a brick wall. By then, it had attracted the attention of Mr. O’Brien and a London-based architect, John McAslan, who together had been batting around ideas for renovation projects with Haiti’s historical preservation institution.