The acquisition would amount to $9.25 per share, a 40 percent premium over Emulex's closing share price Monday.
A spokeswoman for Costa Mesa, Calif.-based Emulex did not immediately return a call requesting comment on the offer.
Meanwhile, Irvine-based Broadcom said it lost $92 million, or 19 cents per share, in the first quarter. That compares with a profit of $74 million, or 14 cents per share, in the year-earlier period. Sales fell 17 percent to $853 million.
Analysts projected a profit of 3 cents per share on sales of $848 million, according to Thomson Reuters.
Broadcom shares tumbled $1.75, or 8 percent, to $20.04 in morning trading, while Emulex saw its stock surge $2.69, or 41 percent, to $9.30.
Broadcom said its unsolicited offer for Emulex, to be funded by cash and marketable securities, would help it develop technology aimed at streamlining computer networks by adding Emulex's expertise in data storage equipment.
"Our combined entity can be a one-stop shop for key networking and storage technologies," Scott McGregor, Broadcom's chief executive, said in a statement.
McGregor said Broadcom approached Emulex about a possible deal in December. Emulex responded in early January, saying the company was not for sale and cutting off talks, according to a letter to Emulex's board released by Broadcom.
Emulex followed by writing a so-called "poison pill" into its bylaws in January. That step was intended to thwart a hostile takeover by giving existing shareholders the right to purchase more stock should any group or individual acquire more than 15 percent of outstanding shares.
Broadcom indicated it would try to get the provision removed. The company plans to ask a Delaware court to invalidate any "improper actions" meant to block Broadcom's takeover bid.