The US online giant announced "Prime Music" will be offered free and without advertising for customers of Amazon Prime, a subscription service that includes free delivery, access to online movies and books and other advantages.
The Amazon music catalogue is far smaller than rival offerings from services like Spotify, which has 20 million songs, but appears to aim for a niche of customers as a new benefit to the Amazon Prime service.
"With Prime Music, Prime members have unlimited, ad-free access to over a million songs at no additional cost to their membership," Amazon said in a statement.
"Prime Music includes tens of thousands of albums from top artists like Daft Punk, Pink, Bruno Mars, Blake Shelton, The Lumineers, Bruce Springsteen and Madonna. And we're just getting started, more music is being added all the time."
Amazon has been rumoured for months to have been working on a music service but reports said talks had been bogged down over royalties and licensing fees.
The New York Times said Sony and Warner Music had agreed to terms with Amazon but that no deal had been reached with the other major music publisher, Universal Music Group, which carries artists such as Lady Gaga and Katy Perry.
The music is an added bonus for customers of Amazon Prime, the annual fee for which was hiked to $99 from $79 earlier this year.
"Prime Music is the latest great addition for Prime members and we think they're going to love it," Amazon chief Jeff Bezos said in a statement.
The move comes after Apple agreed to pay $3 billion for Beats Music to boost its streaming service and compete with the likes of Spotify and Pandora.
The online news site TechCrunch said nine of the top 10 songs on the Billboard 100 were not available for streaming on Amazon.
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