The $5.5 billion deal, which already has won approval in Europe and Japan, is the latest in the chip industry as companies bulk up in response to growing demand for chips in connected devices and cars.
As a condition of approval, Broadcom agreed to build a firewall to prevent the merged company from using information it gains as Cisco System Inc's (CSCO.O) supplier to compete in selling the switches as Cisco's competitor, the FTC said.
Broadcom supplies Cisco, and Brocade competes with Cisco, in making fiber channel switches that transfer large amounts of data between servers and other devices, the FTC said.
Broadcom agreed that the business group which supplies Cisco would work from separate facilities and that a firewall would prevent the use of Cisco's information for any purpose other than supplying Cisco, the FTC said.
Broadcom had no immediate comment. Brocade did not immediately respond to a request for comment.
The deal was announced in November.
Singapore-based Broadcom, formerly Avago Technologies, is known for its connectivity chips used in products ranging from mobiles to servers, while California-based Brocade makes networking switches, software and storage products.
Reporting by Diane Bartz; Editing by Dan Grebler and Jonathan Oatis