Qriocity and the sister PlayStation Network were attacked in mid April by an unknown hacker or hackers and the personal details of around 100 million accounts were stolen, Sony said last month.
The hack was one of the largest ever disclosed by a company, but the damage appears to have been limited to date. Sony said it could not find any evidence that credit card numbers were stolen in the attack, and widespread credit card fraud as a result of the hack has as yet to appear.
From Thursday, users in all countries except Japan should see full Qriocity service restored.
Qriocity links Sony's networked consumer electronics products and delivers music and video programming to compatible devices. It has two main components: Music Unlimited, which delivers streaming music to Sony computers, televisions and the PlayStation 3; and Video on Demand, which sends movies to Bravia TVs.
With the resumption, Sony will be close to fully restoring all network services disrupted by the April attack. The company has already brought back full PlayStation Network service in all territories except Japan, South Korea and Hong Kong.
Partial service is available in the three Asian countries, but they are lagging on full service because Sony has yet to get clearance from local authorities to resume operations.