The acquisition cements the focus by Dell, once a pioneer in the personal computer business, away from hardware like PCs to the more profitable areas of storage and other business services.
"It's a landmark historic deal that really brings them into the enterprise market and makes them a behemoth," said FBR analyst Daniel Ives.
Since going private in 2013, Dell Inc. has been investing in research and development and expanding its software and services business as those in the technology industry continue to struggle with soft PC sales.
"Our new company will be exceptionally well-positioned for growth in the most strategic areas of next generation IT including digital transformation, software-defined data center, converged infrastructure, hybrid cloud, mobile and security," Michael Dell said in a written statement.
Dell will serve as chairman and CEO of the combined company. Joe Tucci, chairman and CEO of EMC, will remain in those roles until the deal is complete.
FBR analyst Daniel Ives called the deal "historic" and said it means Dell is "no longer your grandma's PC company."
"This is a landmark deal that will have wide-reaching ramifications across the tech landscape for years to come," he wrote in a note to clients.
Shareholders of EMC Corp. will receive about $33.15 per share, which includes cash plus tracking stock linked to part of EMC's economic interest in the VMware business. That's a 19 percent premium to EMC's Friday closing price of $27.86.
Cloud computing company VMware Inc., a subsidiary of EMC, will stay an independent, publicly traded company.
Dell Inc.'s headquarters will stay in Round Rock, Texas. The combined enterprise systems business headquarters will be in Hopkinton, Massachusetts, where EMC is based.
The deal, which was approved by EMC's board, is targeted to close in the second or third quarter of Dell's fiscal year ending Feb. 3, 2017. It still needs approval from EMC shareholders.
Dell, started by Michael Dell in 1984 when he was just a teenager, went on to change the PC business with low costs, customized orders and direct sales first over the phone and later the Internet.
EMC's stock rose 83 cents, or 3 percent, to $28.69 in premarket trading about 15 minutes before the market open on Monday.