Apple is expected to make the announcement on Monday in San Francisco at its annual conference for developers, WWDC, the paper said.
It quoted the sources as saying the company had been in talks with banks and retailers about the project since last year.
A spokeswoman at Apple did not immediately respond to a request for comment.
The Telegraph said the iPhone already contains a wireless microchip similar to those found in contactless payment cards, which will allow Apple Pay users to pay by waving the handset over a terminal to pay.
Transport for London, the paper said, was already accepting Apple Pay from American tourists.
Apple at WWDC is also expected to announce enhancements to Apple Pay, including adding the ability to track rewards program information.
Reuters recently surveyed 100 US retailers. Eighty-five supplied detailed responses, and 11 others supplied information only about whether or not they accept Apple Pay. Two did not respond.
While some of the country's top merchants said they use and like the mobile payment system, fewer than a quarter of the retailers said they currently accept Apple Pay, and nearly two-thirds of the chains said categorically they would not be accepting it this year. Only four companies said they have plans to join the program in the next year.
The top reasons retailers cited for not accepting Apple Pay were insufficient customer demand, a lack of access to data generated in Apple Pay transactions and the cost of technology to facilitate the payments. Some merchants said they were holding out because they plan to participate in a new mobile payment system to be launched by a coalition of retailers later this year.
Written with agency inputs