While the application will be free, users will have to sign up for a premium Spotify subscription, which costs 99 kronor ($14) per month.
The Swedish music streaming service has been considered a competitor to Apple's market-leading iTunes store, because it offers a comprehensive, and growing, free library of millions of songs.
Spotify submitted its application to Apple in July, and it was widely anticipated that Apple would reject the advance, due to Apple's dominance of the digital music market.
“We're obviously delighted with the news,” Spotify communications manager Jim Butcher told The Local.
The new application is designed to search for new music, and will allow users to temporarily store playlists on their phone for use when there is no connection. It will also allow users to stream playlists, according to a BBC report.
Spotify's founder and CEO, Daniel Ek, told the BBC that he expected that the new application would bring a big surge in premium subscribers.
The service, which was launched last year, has more than one million Swedish users, and 4.5 million users across Europe, Jim Butcher told The local.
Free Spotify accounts were initially available by invitation only in order to manage the growth rate of the service, however Spotify opened free registration in the UK in February this year. The company has not indicated when free accounts will be available in Sweden. Paid premium subscriptions are open to all.
In an apparent effort to allay concerns about capacity, Ek assured users that Spotify is working on upgrading Spotify's systems. “We're scaling up the systems because response has been tremendous even before the app is available,” he told the BBC.
As well as giving users access to the imminent new Spotify service through the iTunes application on their handsets, Spotify's premium service allows users to run Spotify without advertisements, from anywhere in the world.
And when can music-hungry consumers expect the Spotify application to appear in their iPhone Apps store? Spotify is being tight-lipped: “Soon!”