Users in the Americas and Europe and much of Asia are able to buy and download games online.
Sony Network Entertainment International has also resumed online music services on Qriocity for PlayStation 3, PSP handheld console, VAIO and other PCs.
Details of the "Welcome Back" package programme offered to all registered PlayStation Network and Qriocity account services will be announced by each region, Sony Corp. and Sony Computer Entertainment Inc. said.
Details of the restoration of PlayStation Network services in Japan, Hong Kong, and South Korea, as well as of remaining services on Qriocity will be announced later.
Sony was attacked in one of the biggest data breaches since the advent of the Internet, in which the user names, passwords, addresses and birth dates of more than 100 million people may have been compromised.
The company later suffered attacks on websites including in Greece, Thailand and Indonesia, and on the Canadian site of mobile phone company Sony Ericsson.
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