At a general meeting at Poundland's head office in Willenhall in the West Midlands, 98.4 per cent of investors approved the South African retail giant's revised offer, which it hiked last month from £597m to £610m.
Steinhoff will pay 227p in cash for each Poundland share, of which 225p will be in cash and 2p in dividend.
The deal is scheduled to complete on 16 September.
The enhanced offer is a 43.3 per cent premium to Poundland's share price on 13 June, the day the company originally made its offer.
Poundland’s stock closed up 1.3 per cent yesterday on the news, to 227p – matching the deal’s share price offer.
The buyer was forced to raise its offer after activist investor US hedge fund Elliott, which now owns an almost 25 per cent stake in Poundland, threatened to derail Steinhoff's bid unless the deal was improved.
Poundland's board had given the all-clear to the previous 222p per share offer in July, saying it was a "fair and reasonable" sum.
Last year, Poundland took over its rival 99p Stores in a deal worth £55m.