Poundland, which is headquartered in Willenhall, accepted the 222p-a-share bid after rejecting a cash offer from Steinhoff last month for an undisclosed sum.
The deal comes after Steinhoff - which owns UK furniture firm Harveys and Bensons For Beds - recently lost out in a battle with Sainsbury's to buy Argos owner Home Retail Group in March and was outbid for London-listed white goods retailer Darty.
The sale price, which also includes a 2p-a-share final dividend on top of the 220p-a-share bid, marks around a 40% premium to the value of Poundland's shares in mid-June.
Shares in the business have also soared after it accepted the takeover offer.
The FTSE 250 firm saw its value climb 12.6%, or 24.8p, to 220.8p as it agreed to a £597 million takeover deal despite rejecting an undisclosed cash offer from Steinhoff last month.
It follows a hefty slump in Poundland's shares over the past year after tough trading and a difficult takeover of rival 99p Stores.
Annual results recently laid bare Poundland's sales woes as underlying pre-tax profits fell 13.5% to £37.8 million in the year to March 27, while bottom-line pre-tax profits crashed 83.7% to £5.9 million, including converted 99p Stores.
Steinhoff had already built up a 23.6% stake in Poundland in recent weeks as it stepped up its pursuit of the set-price retailer.
Darren Shapland, chairman of Poundland, said the deal gives investors an "opportunity to realise their shareholding at a certain and attractive price".
He said it achieved the share price value targeted under its turnaround plan earlier than could be expected "against a background of increasing economic uncertainty in the UK and a more challenging trading environment".
Steinhoff chief executive Markus Jooste said: "The board of Steinhoff and its management team are enthusiastic about the opportunities that this transaction brings: we believe that there is significant merit in bringing Poundland into Steinhoff's global network.
"Steinhoff is developing a fast-growing, price-led retail business across the UK and the rest of Europe. Poundland would be a complementary fit to this growth story."
He added that management at Poundland would continue to play a "key role" after the takeover and said he looked forward to "welcoming" the chain's employees.
Poundland has around 18,000 staff across more than 900 stores.
Steinhoff said it had no plans to change the group's head office or employment conditions for staff.
It marks an eventful start at the top for Poundland's new boss, Kevin O'Byrne, after he took the reins earlier this month.
Steinhoff has been determined to expand further across Europe, having tried and failed to gatecrash two deals in recent months.
It is backed by South African retail billionaire Christo Wiese, whose Brait investment group also owns controlling stakes in Virgin Active, New Look and food chain Iceland.
Steinhoff also owns Conforama in France, as well as a number of retailers across Europe, Australasia and Africa.
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