North Korea released three U.S. citizens imprisoned for more than a year and allowed them to fly home with Secretary of State Mike Pompeo, removing a source of diplomatic friction between Washington and Pyongyang ahead of a summit between the leaders of the two adversaries that appeared set for Singapore.

The three men—Kim Dong-chul, Tony Kim and Kim Hak-song—flew out of Pyongyang on Mr. Pompeo’s plane, according to a Twitter message Wednesday morning by President Donald Trump.

The...