News International, the parent company of the newspaper, announced in March it was planning to charge web users to access its content.
Pay-as-you-go access is charged at £1 per day, while signing up to £2 per week subscription means web users can access the website as much as they like.
News International is also running a special introductory offer giving those signing up for the weekly subscription 30 days' access for £1.
"We have been very pleased with the response from readers since the launch," said Rebekah Brooks, chief executive at News International.
"We believe the new sites offer real value and we look forward to continuing to invest and innovate for our readers."
See also: Rupert Murdoch to block Google News