The discount retailer has agreed to a £597m takeover by the South African retail group.
Steinhoff is paying 222 pence per share for Poundland. It made an informal approach to make the deal last month, but the original offer was rejected.
Poundland’s share price had fallen from 418p in February 2015 to below 200p, with pre-tax profits sharply falling.
Shares in Poundland rebounded 12% to 220p on Tuesday, following the news of the takeover.
Darren Shapland, Poundland’s chairman, commented: “The Poundland board believes that Steinhoff’s all-cash offer presents Poundland shareholders with an opportunity to release their shareholding at a certain and attractive price”.
Steinhoff owns 6,500 retail outlets in 30 countries, and prior to the deal it already held a 23% stake in Poundland.