Investors voted at an EGM earlier today and the deal, to be effected by a scheme of arrangement, was also approved at a court meeting.
Dealing in the retailer's shares will be suspended on January 13 and the business delisted four days later.
Peacocks is being bought by its management, led by chief executive Richard Kirk, and backed by hedge funds via acquisition vehicle Henson No 1.
Apart from its eponymous fascia, Peacocks owns the Bonmarché and The Fragrance Shop chains.
In its most recent trading update, covering the five weeks to November 5, Peacocks reported that group like-for-likes were down 0.8 per cent. Good performances from the main chain and The Fragrance Shop were undermined by a 9.4 per cent plunge at Bonmarché.