When Taylor Swift speaks, even the most powerful company in the world listens.

Less than 24 hours after Ms. Swift complained publicly that Apple was not planning to pay royalties during a three-month trial period of its new streaming music service, the company changed course, and confirmed that it will pay its full royalty rates for music during the free trial.

“When I woke up this morning and read Taylor’s note, it really solidified that we need to make a change,” Eddy Cue, Apple’s senior vice president of Internet software and services, said in an interview late Sunday.

In a letter posted Sunday morning to her Tumblr page, called “To Apple, Love Taylor,” Ms. Swift addressed a situation that had begun to send shock waves through the music industry: Apple, which has announced a subscription streaming service to compete with Spotify, Rhapsody and Deezer, was not going to pay royalties during the trial period.

Ms. Swift, who last year pulled her music from Spotify in another dispute over royalties, called Apple’s policy “shocking, disappointing and completely unlike this historically progressive company.”