HPE has offered $12.50 per Nimble Storage share, representing a premium of 45.3 percent to the company's Monday closing price.
Nimble Storage's shares were trading at the offer price before the bell on Tuesday. HPE's stock was unchanged.
HPE will also assume or pay out Nimble's unvested equity awards with a value of about $200 million at close, as part of the deal.
Nimble Storage's entry-to mid-range flash-based products will help HPE cater to customers across all segments, the company said.
HPE Chief Executive Meg Whitman is focusing on a few areas such as networking, storage and technology services since the company was spun off from Hewlett-Packard Co in 2015.
HPE said in January it would buy privately held cloud software company SimpliVity for $650 million in cash.
Sales in HPE's storage business fell 13 percent in its latest quarter. The company also cut its full-year forecast.