The 222p per share offer values the bargain retailer at around £597m, according to the statement issued today. It represents a premium of 39 per cent from 13 June, before the Bensons for Beds and Harveys owner revealed its interest.
Darren Shapland, chairman of Poundland, said that the deal could secure earlier delivery of the group's medium-term value against an increasingly uncertain economic backdrop in the UK and a tougher trading environment.
Its shared popped 12.24 per cent to 219.99p per share at the open.
The company's board believes it is a "fair and reasonable" offer, and will unanimously recommend shareholders approve the scheme at a general meeting. Poundland was advised on the financial terms of the offer by JP Morgan Cazenove and Rothschild.
Markus Jooste, chief executive of Steinhoff, added: "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."
The firm was believed to be having second thoughts about its offer following Britain's vote to leave the European Union.
It initially announced last month that it was considering a bid for Poundland, without the latter's consent.
Its first bid was rejected by the bargain chain store, which Steinhoff subsequently blamed on a slowdown in the company's sales.