Bregal needed 75 per cent of shareholders to approve the deal and secured the required voted on Thursday according to Sky news, which cited people close to the deal.
Warburg Pincus and Bank of Ireland, which previously opposed the sale, agreed to vote in favour of the deal.
RBS, which owns a 15 per cent interest in the business, has been trying to block the deal, saying that the company had not undergone a proper marketing process.
Earlier this year Bregal and fellow private equity firm Quadriga bought German direct marketing specialist LR Health & Beauty Systems from buyout firm Apax Partners.
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