Apple currently dominates the digital music market, which led many to speculate that the app may not be approved.
Credibility
However, many in the music industry regard Spotify as an alternative, and a credible business model for an industry which has had difficulty adapting to the online world.
It is thought that one of the reasons Spotify was so keen to break into the mobile market was the requirement that users pay a subscription charge.
Only about one person in 50 currently pays a subscription, with the rest using the firm's free streaming services.
Spotify, which launched in 2008, now has more than two million users in the UK, and more than six million across Europe.
It has not yet launched in the United States, but says it intends to do so by the end of the year.
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Rory Cellan-Jones tests Spotify's phone music service
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