It isn't clear how much Guvera has paid for the service but the price tag is thought to be less than the £10m Tesco originally forked out.
Blinkbox Music started life as music streaming and radio start-up We7, and was bought by Tesco for £10.8m in 2012.
We7 was rebranded to fit with Tesco's growing Blinkbox media portfolio, which included the original Blinkbox on-demand service, and Blinkbox Books.
A spokesman for Guvera said Blinkbox Music had been acquired debt free, and it was too early to comment on a Blinkbox rebrand or potential staff changes.
The sell-off is part of Tesco's cost-cutting measures, as it disposes of non-core parts of its business.
The supermarket has already sold the biggest arm of Blinkbox, its on-demand film service, to TalkTalk. It is thought Waterstones is currently in talks with Tesco to acquire the ebooks arm of the business.
Guvera is currently not available in Europe, with COO Michael de Vere noting the acquisition would speed up the company's expansion.
He said "The acquisition of blinkbox Music is an important new chapter in the Guvera story, adding significant firepower to our product – both in terms of technical expertise and an established and loyal audience in the UK."