The deal will safeguard 3,000 jobs at the business, which runs the Payless and Barratts chains.
Stylo was put into administration after landlords refused to back a corporate voluntary arrangements proposal.
The 220 stores not acquired by Ziff will be closed imminently, with the loss of 2,500 jobs.
Ziff said: “We were extremely disappointed that the CVAs proposed were not accepted as that would clearly have been the best outcome for all stakeholders, including employees, creditors and landlords.
“We are pleased, however, that we have been able to reach an agreement to preserve some of the business.
“I am confident that the business in its new form, based on a smaller portfolio of stores with an increasing focus on e-commerce, will be able to withstand the brutal conditions on the high street and prosper in the longer term."
Deloitte partner and joint administrator Neville Kahn, said: “Given the difficult trading environment, we are pleased to have achieved a deal."