The offer is only available to new customers who haven't previously taken advantage of a free trial, and you need to sign up by 11th January. Three months after signing up, your subscription will automatically renew for £9.99/$9.99 a month (£7.99/$7.99 for Amazon Prime members) but you can cancel it at any time.
While this free access doesn't bring you Amazon Music HD, you can upgrade to that option for just £4.99/$4.99 per month; a tidy saving on equivalent lossless offerings from Tidal, Qobuz and Deezer.
This deal is for the Individual plan and gives you access to 60 million tracks, thousands of playlists and stations, as well as offline playback and hands-free listening using Alexa. There are also no pesky adverts.
To clarify what you'll get with this Amazon Music tier, it's basically a step up from the standard Amazon Music (which comes free with Prime and gives you 2 million tracks) but it's not as premium as Amazon Music HD, which gives you CD-quality music. You can upgrade to this using the deal above to still make a big saving.
Remember, to get this deal you need to sign up before 11th January.