Avago, which serves the wireless and industrial markets, is offering Broadcom shareholders $17 billion in cash and Avago shares valued at $20 billion. Broadcom makes connectivity chips, for the likes of Apple and Samsung.
It is the biggest deal so far by Avago Chief Executive Hock Tan, who has developed a small chipmaker into a $36 billion company through acquisitions. He has trimmed Avago's portfolio by divesting units while bulking up in faster-growing areas.
The combined company will be based in Singapore and known as Broadcom, will be the third-largest U.S. semiconductor maker by revenue, behind Intel and Qualcomm.
The $37 billion price represents a premium of about 28 percent over Broadcom's market value of $28.85 billion as of Tuesday's close, before the Wall Street Journal reported that the companies were in talks.
Demand for cheaper chips and new products to power Internet-connected gadgets is driving consolidation in the industry.