The PlayStation Network will be fully restored in the US and Europe on 2 June, Sony has said.
The network was shut down in April after Sony discovered a massive security breach that involved the theft of data about 100 million accounts.
A limited service that allowed people to play games has been available since 16 May in many parts of the world.
Full restoration means players can use credit cards to buy games, music and other digital downloads.
The network, which serves both the PlayStation console and Sony's Qriocity music and movie service, is also being fully restored in many Asian nations apart from Hong Kong, South Korea and Japan.
Limited gaming services were also switched on last in those nations as Sony worked to convince the authorities that it had conquered the security shortcomings. Sony gave no date for the full restoration of service in those countries.
Sony said it had beefed up its security systems following the breach and had created a position of chief information security officer to oversee efforts to protect user data.
The attack led to the wide exposure of millions of accounts giving attackers access to login names, passwords and other personal details. Sony said it could not rule out the possibility that attackers had got hold of gamers' credit card details.
However, it said, credit card companies have not reported a rise in fraud following the breach.
The attack is believed to have cost Sony in excess of 14 billion yen (£105m). The cash is being spent to provide insurance cover for gamers, pay for customer support and investigate how the attack happened.
An apology package has been offered to gamers giving them free games, extra days to use premium content and ID insurance.