EMC shareholders will receive $33.15 per share, $24.05 of which will be in cash.
If approved by regulators, the deal would be the biggest in history between two technology companies.
Falling demand for PCs means Dell is looking to expand into more lucrative businesses, and it has identified data storage as a key growth area.
“Our new company will be exceptionally well-positioned for growth in the most strategic areas of next-generation IT ,” Michael Dell said.
EMC CEO Joe Tucci said: “The waves of change we now see in our industry are unprecedented and, to navigate this change, we must create a new company for a new era.”
Michael Dell will be chairman and chief executive of the combined group that, Dell said, would be the world’s “largest privately-controlled, integrated technology company”.
The exact cost of the deal will depend on the value of shares in VMware, the software company controlled by EMC. VMware will remain an independent, listed company.
The price per share agreed represents a 20% premium on Friday’s EMC closing share price of $27.86. EMC shares were up about 4% in pre-market trading on October 12.
The deal is expected to close some time between May and October 2016.
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