STMicroelectronics shares close 1% higher in Paris following the announcement, while Intel shares were up more than 1% on the US market.
Different chips
The two main types of flash memory are called NAND and NOR.
NAND chips are used to store pictures on digital cameras and music on MP3 players, while NOR chips are used to store the software and operating systems on devices such as mobile phones.
Intel has already spun off its NAND flash memory unit into a joint venture with Micron Technology, and says it is still committed to that business.
The new company will own its NOR memory assets, in addition to STMicro's business in both types of memory.
Going public
"Our objective is that this company will go public," said STMicro chief executive Carlo Bozotti.
The companies said that the deal still needed to be approved by regulators and they expected to conclude the merger in the second half of this year.
The new company will start out with $1.3bn worth of debt, much of which it will have used to buy out the flash memory assets of the two companies.
Some analysts are concerned with the amount of debt, especially as it is becoming harder to make money out of NOR chips.
"The NOR part of the market has been unprofitable for a long time and is in decline," said David Manners, components editor of Electronics Weekly.
"They're so keen to get out of the business that they've cobbled together this rather crummy deal," he added.