The deal values Linear Technology at $14.8 billion, or $60 per share.
Ahead of the news, shares of Linear Technology were halted for trade up about 29% at $62 per share. Analog Devices shares were up about 4%.
Stocks across the semiconductor space were broadly higher on Tuesday, with notable gainers including Maxim Integrated (+5%), NSP Semiconductor (+4%), Microsemi (+4%), and Semtech (+3%).
Texas Instruments shares were also up more than 9%. On Monday after the market close Texas Instruments reported earnings that beat expectations.
News of the Analog-Linear deal was first broken by Bloomberg.
Last year, there was a frenzy of multi-billion dollar deals in the tech industry, including Intel's takeover of Altera, Avago's acquisition of Broadcom, and Dell's $67 billion takeover of EMC.
What's driving these deals
What's behind many of these transactions are huge shifts in the way we capture and store data - be it cell phone data, e-commerce data, or any other computer data.
For years, computer data was stored on hard disk drives, which have a CD-like rotating disk. Western Digital, Seagate, and Toshiba all make these. But that technology is being displaced, and companies that pioneered it are watching sales struggle as less-bulky flash memory chips, like those used in phones, become the norm.
One type of flash memory chip is called a NAND chip, and you can find it today in memory cards, USB drives, and "solid state" drives (which look a bit like disk drives on the outside but have no disk or other moving parts on the inside). SanDisk makes these, so Western Digital went out and bought its way into the flash memory market by acquiring SanDisk.
Companies are looking to buy what they don't already build, and the changes mean big tech deals are going to keep coming.
Dell's megadeal has a similar rationale behind it. By acquiring EMC, a data storage company, Dell is taking a big step toward cutting its reliance on personal computers - not to mention moving into the smarter data storage market.
What about 'the cloud'?
You may have heard that "cloud computing" is disrupting traditional data storage.
Yes, the cloud - meaning a network of servers that provide data storage and processing hosted on the internet instead of on local servers or computers - is part of the story. Public cloud providers like Amazon Web Services or Microsoft Azure are also moving towards solid state technologies for their own facilities, and it all leads to tech company mergers.
As we reported last year, we may see more flash memory chip makers - like Micron, Hynix, or even Samsung or Intel - coming together with companies like Seagate. The shift is driven by the need to continue capturing, storing and analyzing a growing amount of data.
Seen in that light, this story is not just about old technology coming together with newer technology. It's about finding ways to continue providing cheap data services that we all use.