The payout includes $17 billion in cash and $20 billion in equity. Avago expects to close the deal in the first quarter of 2016.
Avago CEO Hock Tan said the mega-deal would create "a global diversified leader in communications semiconductors" during a Thursday investor call. Broadcom CEO Scott McGregor said that "size and scale are becoming increasingly important" as the semiconductor industry evolves, and noted that the combined companies would be the third-largest chip company following the deal.
Under Avago's proposal, Broadcom shareholders can opt for $54.50 in cash or stock in the new company.
Broadcom shares fell 2.6% to $55.66 on the news, after rising sharply a day earlier on buyout speculation. Avago fell by less than 1% to $141.
Broadcom develops semiconductors for wired and wireless communications, with applications in voice, video and other products. Customers range from tech manufacturers Samsung (SSNLF) and Hewlett-Packard (HPQ) to cable operators Comcast (CMCSA) and Cox Communications.
Hock said that the post-merger company would have balance between wired and wireless products, and noted that Broadcom's broadband network operations would open up new markets. The combined companies would generate $15.1 billion in sales, compared to Intel's (INTC) $55.9 billion and Qualcomm's (QCOM) $27.5 billion.
Avago has been acquisitive. The Singapore-based chipmaker agreed to buy Emulex for $606 million earlier this year. Last year, Avago bought PLX Technology for $309 million and paid $6.6 billion for LSI Corp.
Wedbush Securities Inc. analyst Betsy Van Hees suggested in a research note that a bidding war is not likely, in part because few companies could acquire a target as large as Broadcom. The analyst said the deal could mirror Avago's purchase of LSI, in which the buyer divested businesses. Avago could drop businesses that Broadcom gained in the $3.7 billion purchase of NetLogic Microsystems, she wrote.
Avago said it will fund the deal through cash on the merger partners' books and from $9 billion in new debt.
David Marcus contributed to this report