The company will "pay artist for streaming, even during customer's free trial period," Eddy Cue, Apple's senior vice president for Internet software and services, wrote late Sunday in a Twitter message.
Cue also tweeted to Swift that Apple hears her and indie artists. Apple will always make sure that artists are paid, he said in another tweet.
Swift tweeted in response: "I am elated and relieved. Thank you for your kind words of support today. They listened to us."
Apple Music, which is scheduled to launch on June 30, comes with a three-month free trial, which is to be followed by a monthly subscription of US$10, and a family subscription, valid for up to six members, for $15 a month. Unlike rivals like Spotify, the company will not offer music that comes free with advertisements.
Swift wrote in a blog post Sunday that she was holding back her album "1989" from Apple Music, saying that "three months is a long time to go unpaid, and it is unfair to ask anyone to work for nothing." She said hers were "not the complaints of a spoiled, petulant child," but echoed the sentiments of artists, writers and producers in her social circles "who are afraid to speak up publicly because we admire and respect Apple so much." The pop star said she was speaking for people like new artists and young songwriters for whom the royalties mattered.
Swift said that Apple had the money to pay artists, writers and producers even if it wasn't collecting money from users during the trial period.
Apple's decision had been criticized in many circles, with complaints mainly coming from independent labels operating on tight budgets.