The two new stations will be Apple Music Hits, playing popular songs from the 80s, 90s and 2000s, and Apple Music Country, focusing on country sounds.
The tech giant launched its music streaming service in 2015, which included the Beats 1 radio station, fronted by former BBC Radio One DJ Zane Lowe.
It has grown to include shows from the likes of Sir Elton John, Billie Eilish and Lady Gaga.
British R&B star Estelle has been confirmed among the daily hosts on Apple Music Hits.
Lowe, who is also Apple Music’s global creative director, said: “Apple Music is home — it’s home to artists, it’s home to fans, and it’s home to incredible music.
“I’m an obsessive music nerd. I love searching for the most exciting new artists and playing them right alongside the most essential, established artists of our time, because great music does not know the difference and Apple Music fans just want to hear great music. That’s what Apple Music radio is all about.”
Oliver Schusser, vice president of Apple Music, Beats and international content, said the company hoped to continue to invest in live radio.
“For the past five years, if ever there was a meaningful moment in music culture, Beats 1 was there bringing human curation to the forefront and drawing in listeners with exclusive shows from some of the most innovative, respected and beloved people in music,” he said.
“Now, Apple Music radio provides an unparalleled global platform for artists across all genres to talk about, create and share music with their fans, and this is just the beginning. We will continue to invest in live radio and create opportunities for listeners around the world to connect with the music they love.”