The agency is thought to have beaten shops including MediaCom in the competitive pitch.
Starcom Mediavest Group, which held the business in markets including the US and the UK, was dropped in the US last year. Spotify moved the US account to 360i, the Dentsu Aegis Network digital agency. SMG did not take part in the UK process.
Spotify does not have a creative agency of record but is understood to work with a number of shops on a project basis, including Wieden & Kennedy and Razorfish.
The company spent an estimated £2.5 million on media in the UK in 2014, including a TV campaign on The X Factor, but cut expenditure last year. It is poised to increase media spend as it competes with Apple, Google, Deezer, Pandora and other rivals.
Spotify offers a free membership with advertising or a monthly paid subscription with no ads.
Goodstuff and Spotify declined to comment.