The acquisition was announced on 8 August.
Mattress Firm president and CEO Ken Murphy said: “The transaction with Steinhoff is complete and I am delighted that Mattress Firm is now part of the Steinhoff organisation.
“Steinhoff has a proven track record in the global mattress industry, and they share our vision for the growth and expansion of Mattress Firm.
"This is an exciting event for our customers, employees and business partners as we enter a new chapter for Mattress Firm. Our team remains committed to building a national chain under one banner in the US and offering our guests a great night’s sleep.”
The acquisition of Mattress Firm was completed concurrently with payment for the earlier tendered shares in accordance with the agreement through a merger of an indirect wholly owned subsidiary with Mattress Firm.
All shares of Mattress Firm common stock not purchased in the tender offer will be converted into the right to receive $64.00 a share.
Following completion of the transaction, the retailer's common stock will no longer be traded on the NASDAQ stock market.
With the closure of the deal, Mattress Firm became a subsidiary of Steinhoff.
Led by executive chairman Steve Stagner and president and CEO Ken Murphy, Mattress Firm’s management will remain in place and continue to run its day-to-day activities.