Ireland will vote this spring on whether to overturn a constitutional abortion ban, in a referendum likely to be hotly contested as the country moves away from the conservatism of a Catholic Church tarnished by a sex abuse scandal and other controversies.

With opinion polls pointing to a narrow vote in favor of change, the government’s announcement late Wednesday that the referendum will be held May 25 marks the official start of a campaign over whether to allow abortion in one of the few European countries that still outlaws...