The US tech giant forged the agreement with Taiwan Semiconductor Manufacturing Co (TSMC) earlier this month, according to the Wall Street Journal, which cited unidentified TSMC executives.
It said manufacturing of the chips, to be used in Apple mobile devices, would start early next year.
The Journal said the move is the latest in a series of efforts by Apple to lessen its reliance on parts produced by South Korea's Samsung.
But despite the deal with TSMC, Samsung will remain Apple's main supplier of high-resolution screens, memory chips and processors used in mobile devices through next year, the Journal said.
TSMC spokeswoman Elizabeth Sun declined to comment when approached by AFP.
"In line with the company's established policy, we will not comment on individual clients," she said.
Analysts see the deal as part of Apple's bid to diversify its supply chains and distance itself from Samsung, its main competitor in the mobile phone market.
"It is inevitable that Apple must move to reduce its reliance on Samsung while their legal lawsuits over patents flare," an analyst at a foreign firm in Taipei told AFP, declining to be named.
Samsung won a round in its long-running patents battle with Apple in early June when a US trade panel banned the import and sale of some older models of the iPhone and iPad.
In a separate patent fight in US federal court, Samsung was ordered last August to pay more than $1 billion for patent infringement. A judge later slashed the award to $598.9 million.
By diversifying its supply chains, Apple could also cut its costs, Kuo Ming-chi, analyst at the Taipei-based KGI Securities Investment Advisory Co, told AFP.
"This is crucial as Apple's profit margin fell to around 37 percent in the first quarter, down from a peak of around 45 percent."
Kuo said the diversification policy was also reflected in Apple's movement of some of its assembly orders away from Taiwanese manufacturing conglomerate Hon Hai, also known as Foxconn.
Hon Hai employs about one million workers in China, roughly half of them based in its main facility in Shenzhen bordering Hong Kong.
Apple and TSMC started discussing working together to build chips as early as 2010, according to the Journal report.
Apple asked either to invest in TSMC, or to have TSMC set aside factory space dedicated to Apple chips, it said.
But both requests were rejected as the Taiwanese company wanted to maintain its independence and manufacturing flexibility, the Journal said.