The combined entity will have annual revenues of 4.5 billion US dollars (£3.4bn), creating one of the biggest software firms in the UK.
Micro Focus executive chairman Kevin Loosemore, who will head up the new firm, said: "The merger will create one of the world's largest infrastructure software companies with leading positions across a number of key products and represents a compelling opportunity to create significant value for both companies' shareholders by applying Micro Focus' proven approach to efficient management of mature software products."
The deal includes Autonomy Corp, which HPE acquired for 11 billion US dollars in 2011, before writing off three-quarters of its value.
Micro Focus, which has its headquarters in Newbury, Berkshire, has embarked on a series of acquisitions under Mr Loosemore. In 2014 it snapped up Attachmate for 1.2 billion US dollars and bought Serena Software this year for 540 million US dollars (£403m).
In July, Micro Focus reported pre-tax profits of 195 million US dollars (£145.7m) and revenue of 1.2 billion US dollars (£896.4m).
The merger comes months after Japan's Softbank's acquired ARM Holdings, widely regarded as the jewel in the crown of the UK technology sector, for £24.3 billion.
Neil Wilson, markets analyst at ETX Capital, said: "It's a big scalp for the FTSE 100 group. HPE will no doubt be glad to see the back of Autonomy, which it acquired in 2011 for 11 billion US dollars in one of the worst deals in recent corporate history.
"After ARM Holdings was sold to SoftBank, it's also a sign that the UK tech sector is still capable of making deals in the other direction. It's a confident move - it would be the biggest acquisition by a British company of a foreign tech firm - and comes in the face of a massive drop in the value of the pound that has made UK firms the target of overseas bidders."
Our BQ Bulletin emails will land in your inbox at 7.30am, Monday to Friday, with a mix of the latest local business news, national news, and features to inspire you. Sign up here!
Click here to read our privacy statement