HPE's stake in MphasiS could be valued as high as $1.1 billion (£770m), with low estimates at $825 million (£580m). It will be for at least 84 percent of HPE's 60.5 percent stake of MphasiS.
Rumours had been floated earlier this year that HPE was set to sell its 60.5 percent stake in the Bangalore offshore services subsidiary.
There were a few competing candidates in both the IT services industry and in private equity, according to analysts at TechMarketView, but it was financial services and asset management firm Blackstone that closed the sale.
India's IT services industry is still booming, as businesses around the world continue along the path of outsourcing services into the country. This sale is tipped to be one of the largest in the country's sizable outsourcing sector, worth as much as $150 billion.
The deal follows Blackstone's purchase of a minority stake in another Indian IT business, IBS Software, late last year.
"From HPE's perspective, the sale makes particular sense in the context of its recent split from HP Inc," analysts at TechMarketView said. "It helps CEO Meg Whitman continue to bring focus around the HPE offerings, while providing an injection of cash."
"Blackstone has indicated it could send up paying up to $1.1 billion in all," TechMarketView said. "The deal, therefore, looks to be a good move for HPE."
Mike Nefkens, GM of HPE Enterprise Services, said in a statement: "While our financial relationship is changing, the business and commercial relationship with Mphasis remains an important part of our service delivery strategy. We remain committed to our strategic partnership with Mphasis and to providing our customers with the high level of service and support they expect from HPE."
In September last year, HPE cut 30,000 staff in a bid to save $2.7 billion for the newly split business.
HPE rival Dell recently announced the sale of its IT services business, Dell Services, to Japan's NTT.
As well as raising additional cash in the run-up to Dell's merger with EMC, the move was noted as part of wider plans to realign the business with its core services in enterprise systems and hardware.