When London-based AstraZeneca rejected Pfizer Inc.’s $119 billion takeover offer in late May, it put the kibosh on the U.S. drug-maker’s attempt to create the largest pharmaceutical company in the world—and also to slash its corporate income tax bill.

The effort was the highest-profile example to date of an attempted “inversion” transaction, in which U.S. companies seek to acquire or merge with foreign companies so they can incorporate elsewhere to escape U.S. federal tax rates of up to 35 percent. The United Kingdom and Ireland are particularly attractive destinations, although not the only ones.