There was no evidence the hackers used the passwords they obtained to pursue information not connected to the Wen family investigation, The Times said, adding that no customer data were stolen.
The Times said it informed and "voluntarily briefed" the FBI about the attacks.
An angry reaction last year
At the time of the publication of the initial Times report on Wen's family in October, Chinese authorities called it an attempt "to blacken China's image," saying it had "ulterior motives."
It came at a particularly sensitive time in China, a matter of weeks before the start of the ruling Communist Party's 18th National Congress, at which the country's next set of leaders was announced.
The Times' English- and Chinese-language websites remain blocked in mainland China, as do those of Bloomberg News, which in June published a report on the business interests of relatives of Xi Jinping, who is now the country's top leader.
The Chinese government tries aggressively to control the flow of information inside its borders about sensitive topics like unrest in Tibetan areas and criticism of senior officials. It strictly manages the output of domestic news media outlets and has a history of shutting off access to international news websites.
Chinese authorities have blacked out the broadcast signal for international television stations like CNN and the BBC when they have aired sensitive reports about the country.