The group - which owns Topshop, Burton and a raft of other high street brands - announced that its company voluntary arrangements (CVAs) had all been voted through at a reconvened meeting of creditors.
It means around 1,000 jobs are at risk as 23 stores close under the CVA, while another 25 will be shuttered as part of a wider restructuring.
Landlords will also receive smaller amounts of rent on certain properties, with some reduced to half the original price.
The proposals were passed at a second meeting on Wednesday, which came a week after the first was postponed.
The initial vote was adjourned after it became clear that there was not sufficient support among landlords. Sir Philip Green and his wife Lady Green then proposed less severe rent cuts in a bid to appease the opponents of the proposals.
However, the CVA remained contentious, with some landlords reported to have voted against.
Arcadia's chief executive Ian Grabiner said: "We are extremely grateful to our creditors for supporting these proposals and to Lady Green for her continued support.
"After many months of engaging with all our key stakeholders, taking on board their feedback, and sharing our turnaround plans, the future of Arcadia, our thousands of colleagues, and our extensive supplier base is now on a much firmer footing.
"From today, with the right structure in place to reduce our cost base and create a stable financial platform for the Group, we can execute our business turnaround plan to drive growth through our digital and wholesale channels, while ensuring our store portfolio remains at the heart of our customer offer.
"I am confident about the future of Arcadia and our ability to provide our customers with the very best multi-channel experience, deliver the fashion trends that they demand, and ultimately inspire a renewed loyalty to our brands that will support the long-term growth of our business."
Speaking to the press after the meeting but before the result, Oliver Buhus from supplier Paragon Clothing said landlords had been "ruthless and self-serving".
"There's no sense of taking an initiative to act collectively, it's each landlord for himself," he said.
The proposals, which were launched last month, involve the closure of 23 stores in the UK and Ireland.
Another 11 Topshop and Topman stores in the US were earmarked for closure, while an additional 25 Miss Selfridge and Evans stores were also slated to be axed. In total, at least 1,000 employees are likely to be affected.
The initial plans also included a reduction in the company's contributions to its pension fund, alongside a fresh injection of cash into the scheme.
However, Arcadia agreed with the pensions watchdog last week that Green would contribute another £25 million - bringing the total cash and security package to the value of £310m.
Responding to the decision, Melanie Leech, chief executive of the British Property Federation, said: "CVAs are never easy as property owners are being asked to absorb large losses, which impacts the investment that these owners manage, including many of our savings and pensions. However, ensuring a sustainable future for the UK retail sector is equally critical to both the property and retail sectors.
"Property owners will now want to see Arcadia's leadership committed to delivering its turnaround plan to restore the long-term health of the business."
Meanwhile Chloe Collins, senior retail analyst at Global Data, said: Although Arcadia's CVA has been approved, it is unsurprising that it faced backlash from some landlords who have doubts about the retailer's future.
"Its leading brands - Topshop and Topman - still have a strong following among millennials, however many of the other, such as Miss Selfridge and Dorothy Perkins, are now irrelevant in a highly saturated market and chances of revival are slim, leading landlords to question whether other retailers could offer their spaces more longevity."
Speculation began early this year that Green would look to either sell off the company, or close stores.
In March, Arcadia confirmed it was exploring options to improve efficiency in the business.
Later that month, it hired property advisers to assess its estate while drawing up restructuring plans.
In April, US investor Leonard Green & Partners sold its 25 per cent stake in Topshop and Topman back to the parent company, in a move which Arcadia said simplified its structure and would allow the board to focus on restructuring.
The news comes just weeks after Green failed to appear on the Sunday Times Rich List for the first time in 17 years.
His reputation has been left damaged by the 2016 collapse of BHS, which resulted in the loss of 11,000 jobs.
The tycoon faced criticism for his handling of the retailer and eventually agreed to pay £363m of his own money into the its pension pot.