Swift had said the plan was “unfair”, arguing Apple had the money to cover the cost.
“I find it to be shocking, disappointing, and completely unlike this historically progressive and generous company,” the 25-year-old said, describing Apple as one of her “best partners in selling music”.
“Three months is a long time to go unpaid, and it is unfair to ask anyone to work for nothing.
“We don’t ask you for free iPhones. Please don’t ask us to provide you with our music for no compensation.”
In response apple music executive sent a tweet toward Swift reading “We hear you @taylorswift13 and indie artists. Love, Apple,”
After hearing news of the company’s decision on Sunday night Swift tweeted: “I am elated and relieved. Thank you for your words of support today. They listened to us.”
The music industry has generally supported the company bringing its vast music library to paid streaming, and the firm said it would pay 73% of the music subscription revenue to music owners.
Apple Music launches on 30 June. It will cost $9.99 (£6.30) per month in the US for one person or $14.99 for families.