Poundland has agreed to a higher 227p-a-share bid, worth £610.4 million including a 2p-a-share dividend, following moves by Elliott Management to build up a 17.5% stake in the group.
Steinhoff had originally agreed a 222p-a-share deal worth £597 million last month, but within days the US activist had increased its stake, reportedly with plans to bump up the deal - so-called "bumpitrage".
Poundland and Steinhoff remained tight-lipped on Elliott's involvement in the higher offer.
Darren Shapland, chairman of Poundland, said: "The Poundland board is pleased to recommend Steinhoff Europe's increased all-cash offer which presents Poundland shareholders with an opportunity to realise their shareholding at an improved price."
Steinhoff said its revised offer was final.
Markus Jooste, chief executive of Steinhoff, added: "By offering Poundland shareholders an improved cash offer we aim to bring certainty to the transaction recognising the strength and value of the business and its management team."
Elliott has a track record of "bumpitrage" and muscling in on takeovers, having played a part in pushing for a better offer from brewing giant Anheuser-Busch InBev for SABMiller.
It also succeeded in getting a higher offer for Quintain - the UK property group that developed Wembley Stadium - last year from US buyout firm Lone Star.
Steinhoff, which owns UK furniture firm Harveys and Bensons For Beds, has been determined to expand further across Europe.
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.
Poundland has around 18,000 staff across more than 900 stores.
If you’ve enjoyed this article, click on the link below to sign up for more similar stories in your area.