Royal Dutch Shell PLC agreed Monday to pay $15.5 million to settle a lawsuit over the 1995 deaths of Nigerian author and activist Ken Saro-Wiwa and others.

The Anglo-Dutch oil giant faced a lawsuit in federal court in Manhattan under the Alien Tort Claims Act, on allegations that it was complicit in the 1995 deaths of Mr. Saro-Wiwa and other activists. The lawsuit was brought by family members and surviving activists.

Shell...