TEHRAN—A year ago, the president of Iran's chamber of commerce could go more than a month without hosting a foreign business delegation, due to their fears of violating economic sanctions. These days, Gholam Hossein Shafei greets trade missions from the Middle East, Asia and Latin America almost every day and travels to European capitals.

"We have a new environment domestically, and a new look from the outside," the 63-year-old said from his expansive offices in central Tehran, which overlook the abandoned American...