Micro Focus said the move was a rare opportunity to expand significantly, with the combined business expected to have annual revenue of US$4.5bn and underlying earnings of US$1.35bn.
It also said it anticipated the deal would improve adjusted earnings per share by the end of the first full year after completing the deal.
HPE is hiving off the division as part of a drive to switch its focus to networking, storage and technology services following its split last year from computing and printer giant HP.
Micro Focus chairman Kevin Loosemore said: "Today's announcement marks another significant milestone for Micro Focus and is wholly consistent with the long-term business strategy we have been pursuing. The merger will create one of the world's largest infrastructure software companies."
President and chief executive of HPE, Meg Whitman, said: "We believe the software assets that will be a part of this combination will bring better value to both our customers and shareholders as part of a more focused software company."