European Union finance ministers have selected their nominee to be the next chief of the International Monetary Fund in a move that would require a change of the institution’s rules.

Kristalina Georgieva, the Bulgarian chief executive of the World Bank Group, was chosen in a secret ballot on Friday evening as the group’s preferred candidate for the job, according to France’s finance minister Bruno Le Maire. Ms. Georgieva has also served as vice president of the EU’s executive body.

If...