The acquisition will be done through Marble II Pte, part of Blackstone Group.
In April this year, Blackstone had said it will buy out 50% stake of HP Enterprise in Mphasis for up to Rs 7,071 crore ($ 1.1 billion), marking the largest IT deal for the US-based firm in India.
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CCI, which keeps a tab on unfair business practices, has cleared the deal, as per the regulator's website.
Marble II Pte is a special purpose vehicle and is currently not engaged in any business activity. Blackstone is a global alternative asset manager and provider of financial advisory services.
Mphasis is an IT solutions provider, offering applications, business process outsourcing and infrastructure services globally through a combination of technology knowhow, domain and process expertise.