For several years, as Europe’s migration crisis grew, investigators pursued one of the world’s most wanted people smugglers, a fugitive known as “the general” for the efficiency of his network.

Police from five nations tracked Medhanie Yedhego Mered as he crisscrossed the Sahara ferrying compatriots from Eritrea, his home country on the Horn of Africa, to Europe. In May of last year they finally zeroed in on him, drinking an...