The nationalised bank agreed to sell Hypo Alpe Adria Bank AG, the unit which operates in the southern Austrian province of Carinthia, to Anadi Financial Holdings, the Klagenfurt-based lender said in a statement.
London-based Kanoria, 49, is the brother of Hemant Kanoria, chairman of Indian group SREI Infrastructure Finance Limited, which had been named by the Austrian media as a potential buyer of the bank.
"New products, additional markets and fostering the core region are the aims of our engagement," Kanoria, who is also a doctor, said in the statement, adding that SREI will provide "financial expertise" to the business.
The sale - the first step in the bank's campaign to divest operating units under pressure from the European Commission - is now subject to regulatory approval.
The sale was managed by JPMorgan Chase & Co and TJP Advisory & Management Services, Hypo Alpe said.
The Hypo Group is also in the process of shedding its subsidiaries in south-eastern Europe after it ran into trouble before the global financial crisis because of risky investments.