LONDON—BP PLC will return to northern Iraq for the first time since Islamic State swept through the region three years ago, potentially heralding a new era of stability in one of the world’s most dangerous energy-production provinces.

The move thrusts BP back into a volatile region that it fled along with Iraqi forces in 2014 as Islamic State approached. Iraqi Kurds, who have a semiautonomous region of the country nearby, defended and held Kirkuk and its oil fields for about three years but quickly ceded them in October when...