Chip maker Avago Technologies Ltd. agreed to buy rival Broadcom Corp. for $37 billion in cash and stock, the latest in a wave of deals for the companies that supply parts to power smartphones, tablets and other gadgets.

Avago will pay $17 billion in cash and about $20 billion of its own shares.

Broadcom investors can choose to receive $54.50 a share in cash or about 0.44 shares in a newly formed Singapore holding company, among other options. They will own about 32% of the combined company.

After the deal closes, expected by the first quarter of next year, the company will adopt the name Broadcom Ltd. and continue to be led by Avago Chief Executive Hock Tan.

Shares of Broadcom edged down 1.8% to $56.13 premarket after surging 21% on Wednesday when The Wall Street Journal reported the companies were in advanced talks. Avago edged up 1.3% premarket after rising 7.8% on Wednesday.

The deal comes as technology stocks are surging and investors on Wednesday pushed the Nasdaq Composite Index up to a record closing high. At the same time, large chip makers are turning to acquisitions after struggling with anemic revenue gains.

Growth has been hard to come by for Broadcom, a 24-year-old company that makes communications chips for tablets and smartphones, and supplies the Internet links for cable-television and telecommunications devices. It earned $1.41 billion last year but has struggled to lift sales. Its revenue was up just 1.5%, to $8.4 billion.

Avago, the acquisitive former semiconductor unit of Hewlett-Packard Co., makes chips for wireless-communications and corporate-data-storage markets. Based in San Jose, Calif., and Singapore, it reported $4.3 billion in sales in the 12 months ended Nov. 2.

The combined company will have $15 billion in annual revenue.

Neither Avago nor Broadcom has the kind of dominance over individual markets that better-known rivals such as Intel Corp. and Qualcomm Inc. enjoy, and a merger could help address that. In addition to consumer applications, Broadcom supplies the vast majority of chips used in the latest networking switches found in corporate data centers, a fast-growing business that could enhance Avago's communications-focused revenue stream.

Broadcom was co-founded by a team led by engineers Henry Samueli, who remains chairman and chief technology officer, and Henry Nicholas III, a former chief executive who stepped down in 2003. Mr. Nicholas held about 25% of Broadcom's voting shares as of the end of March, according to the company's most recent proxy statement. Mr. Samueli held about 22%.

Avago once was part of Agilent Technologies Inc., which spun off from H-P in 1999. Agilent later sold what's now Avago to private-equity firms Silver Lake, KKR & Co. and other investors in a $2.66 billion buyout.

Avago went public in 2009 after having incorporated in Singapore, which is known for having a low corporate tax rate. In its last fiscal year, Avago had a tax rate of less than 10%, according to its annual report. In contrast, the U.S. statutory corporate tax rate is 35%.

The company has been one of the more aggressive acquirers in the semiconductor sector in the past two years, though a deal for Broadcom would be by far its biggest ever. Since 2013, the company has purchased five companies in the U.S. valued at about $8 billion in total, including the acquisition last year of rival LSI Corp. for $6.6 billion. Earlier this year, it bought Emulex Corp. for around $600 million. In that span, its market cap has risen by more than $25 billion as investors cheer the rapid-fire deal making. This year,

Avago has been likened to health-care companies such as Valeant Pharmaceuticals International Inc. that are based in foreign tax jurisdictions and have become voracious acquirers.

An acquisition of Broadcom that was valued at $35 billion would be one of the largest semiconductor takeovers ever, according to researcher Dealogic, and would come amid a burst of deals among such companies. So far this year, there have been more than $26 billion in semiconductor deals announced globally, not including any tie-up between Broadcom and Avago, according to Dealogic. That is more than double the volume in the same period last year, and the largest year-to-date total since Dealogic started keeping records in 1995.

In March, NXP Semiconductors NV agreed to buy Freescale Semiconductor Ltd. in an $11.8 billion deal. Intel Corp. also is in talks to buy Altera Corp., which has a roughly $14 billion market value. Talks between those companies have been off-and-on and it is conceivable they won't reach a deal, according to a person familiar with the matter.

Meanwhile, Qualcomm Inc. has come under pressure from activist investor Jana Partners LLC, which is pushing the chip giant to pursue a breakup, among other actions.

Separately, Avago reported Thursday that its revenue for the quarter ended May 3 more than doubled to $1.61 billion, though that was still short of analysts' call for $1.64 billion. Per-share earnings from continuing operations were $2.13 a share, beating estimates of $2.01 a share.

--Chelsey Dulaney contributed to this article.

Write to Dana Mattioli at dana.mattioli@wsj.com, Dana Cimilluca at dana.cimilluca@wsj.com and Shayndi Raice at shayndi.raice@wsj.com

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