Sony said it would begin a phased restoration of its PlayStation Network games service on Sunday on a country by country basis and expected the process to be complete by May 31.
The company said phased restoration of the Sony Online Entertainment PC-based online games service would also begin on Sunday.
The Japanese electronics and entertainment giant apologised to customers for the outages and said in a statement a range of new security measures had been introduced.
I can't thank you enough for your patience and support during this time, Sony No. 2 Kazuo Hirai said in the news release, acknowledging that customers were anxious to use their prroducts again.
We are taking aggressive action at all levels to address the concerns that were raised by this incident, and are making consumer data protection a full-time, company wide commitment.
Sony discovered on April 19 its PlayStation Network, which enables PlayStation games console owners to download games and pit their skills against rivals, had been breached by hackers, who accessed personal details on 77 million accounts.
It shut down the network and its Qriocity online music and movie service, frustrating many users, but later found out that a separate online games service had also been accessed, forcing a further shutdown.
Users of the Sony Online Entertainment service will be offered free game time as compensation for the outage, the company said.
(Reporting by Isabel Reynolds; Editing by Ron Popeski)