"Our new company will be exceptionally well-positioned for growth in the most strategic areas of next-generation IT ," said Dell boss Michael Dell.
EMC boss 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".
The deal will make Dell the largest privately-controlled, integrated technology 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 Monday.
"Dell wants to become the old IBM Corp, a one-stop shop for corporate clients," said Erik Gordon from the University of Michigan's Ross School of Business. That model fell apart a couple of decades ago. Reviving it would be a stunning coup for Dell."