The New York company also posted a wider loss and said Chief Executive Philip Krim stepped down.
The purchase price represents a 94% premium over the stock's Friday closing price. Casper shares were up 88% to $6.68 at last check.
The stock in June touched a 52-week high $12.
Casper's board unanimously approved the terms. The deal with the New York investment firm is expected to be completed in the first quarter, pending approval by Casper holders.
Officers and directors of Casper Sleep, as well as affiliated investors, holding a total of 28% of the company have agreed to vote for the deal.
"In consultation with outside advisors, Casper’s board determined that "the transaction proposed by Durational is superior to all other alternatives available," Krim said in a statement.
Casper Sleep also reported that its third-quarter net loss widened to $25.3 million, or 61 cents a share, from $16.1 million, or 40 cents, in the year-earlier quarter.
Revenue of $156.5 million, was 27% higher than the year-earlier figure.
Analysts polled by FactSet were expecting a net loss of 43 cents a share on revenue of $156.2 million.
The company said that industrywide supply-chain challenges resulted in inflation pressures and hurt its ability to meet demand.
Casper withdrew its guidance for the rest of the year.