Amazon Music Unlimited will offer "tens of millions of songs" to subscribers, the company said, a step up from the two million available on its existing Amazon Prime streaming service.
The new service costs USD 9.99 a month - the same as rivals Spotify Premium, Apple Music and Google Play - but Amazon is offering a discounted rate of USD 3.99 for subscribers who limit use to its voice-controlled Echo speakers.
Music streaming has boomed this year, with the number of streams more than doubling in the first six months of the year compared to the same period last year, according to trade specialists BuzzAngle Music.
Amazon's new US offering comes a month after Sweden's Spotify said it had passed 40 million paying subscribers, consolidating its position as world leader in the streaming sector.
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Spotify stands well clear of its nearest rival Apple Music, which had some 15 million paying subscribers in June, but it has yet to post an annual profit, spending most of its revenue on compensating artists and rights-holders.
Tidal had a major boost earlier in the year when Beyonce - who is married to Jay-Z - released her album "Lemonade" exclusively on the service.
The new Amazon service is scheduled to launch in Britain, Germany and Austria later this year.