Mr Day, who is owner of The Edinburgh Woollen Mill Group, has acquired more than half of the company's shares, triggering a mandatory takeover bid.
Acting through holding company Spectre, the businessman bought more than 26 million shares, representing 52.4% of the company.
At just 11.445p per share, the offer represents a significant discount on the company's Monday closing price of 18p and values the whole entity at just £5.7 million.
Shares in the company were down 15.7% at 15p in early trading on Tuesday.
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Spectre said it would undertake a profitability assessment on Bonmarche's estate of more than 300 stores and shutter underperforming sites or reduce costs by cutting the number of staff or seeking a lower rent.
It comes after Bonmarche issued its third profit warning in just six months in March.
The womenswear retailer said it has seen "significantly weaker" trading since the start of the month, reversing a bounce-back in January and February after it resorted to heavy discounting to shift stock.
In a statement relating to the takeover offer, Spectre said: "Against the backdrop of the significant decline in Bonmarche's profitability, Spectre believes it is well positioned to provide advice, guidance and support to secure the long term future of the Bonmarchebusiness, its stores and employees.
"The owner of Spectre, Philip Day, has a successful track record within the retail sector, especially in turnaround and distressed situations."
Mr Day's name has been linked with several retail turnarounds. At the weekend he was named as a bidder in the race for collapsed womenswear brand LK Bennett, though he later withdrew from the process.
Last year he was one of the potential buyers circling House of Fraser, which was eventually sold to Sports Direct owner Mike Ashley.
His other investments include Peacocks, Proquip, Austin Reed, Country Casuals, Jaeger and Jacques Vert.
Maureen Hinton, global retail research director at GlobalData, said: "This is an excellent result for Bonmarche, which is struggling following profit warnings and a challenging market. It rejoins its former sister company Jane Norman which Day saved several years ago and continues to trade.
"Being taken out of constant City reporting and scrutiny will allow the retailer to take a long-term view of the business and benefit from the shared assets of the Edinburgh Woollen Mill group."