ABUJA, Nigeria—Eighty-two of the nearly 300 Chibok schoolgirls seized three years ago by Boko Haram were freed in exchange for detained members of the jihadist group, the biggest breakthrough in the effort to recover the insurgency’s most-famous captives.

Dozens of the women—dressed in brightly colored dresses given to them by Nigerian authorities upon their release—were escorted to Abuja by soldiers on Sunday for an audience with President Muhammadu Buhari before being reunited with their families. Media access was restricted,...