Hewlett Packard Enterprise Co. said Tuesday it agreed to acquire Nimble Storage Inc. for about $1 billion in cash, aiming to ignite sales in its declining storage business.

The deal also calls for HP Enterprise to assume or pay out Nimble’s unvested equity awards with a value of about $200 million at closing. The cash amount is about a 41% premium to Nimble’s roughly $700 million market value as of Monday’s close of trading.

Nimble...