Throughout Monday and most of Tuesday, the personal banking site was not allowing customers to log on, while business accounts were running slowly.
HSBC said business and personal customers had been able to log on since Tuesday evening.
In a video posted on Twitter, the bank's chief operating officer, John Hackett, again apologised to customers.
"We continue to monitor the service very closely, and are ready to respond should any issues arise, but all the evidence is positive," he said.
But the bank, which has 17 million customers, has still not given a precise explanation as to what went wrong.
It blamed the problem on a complex technical issue within its banking and mobile systems.
Mr Hackett said that no one's personal data was put at risk during the failure, and that all customers would be compensated for losses caused by it.
The chair of the Treasury Select Committee, Andrew Tyrie, promised to grill HSBC's chief executive on why such failures keep occurring.
HSBC was hit by a previous IT glitch in August 2015, which prevented 275,000 payments going through just ahead of the Bank Holiday weekend.
HSBC says all its online banking services are operating at full capacity again, after two days of disruption.