NEW YORK — Tempur-Pedic International has agreed to buy Sealy, based in Randolph County, for about $229 million, combining the two biggest publicly traded mattress companies and ending a more than 20-year run of private-equity ownership.

The offer of $2.20 a share is 2.8 percent more than Sealy’s closing price Wednesday. Tempur-Pedic, a pioneer of memory-foam mattresses based in Lexington, Ky., will assume or repay all of Sealy’s outstanding and convertible debt, for a total deal value to $1.3 billion, according to a statement Thursday.

Mattress makers had been popular targets for private-equity firms until the economic crisis led to a slump in demand for high-priced bedding products. Tempur-Pedic, which a decade ago was owned by TA Associates Inc., is gaining brands including Sealy Posturepedic and Stearns & Foster from Sealy, which dates back to 1881 and is 44 percent owned by KKR & Co.

Sealy, which has had five buyout-firm owners since 1989, was acquired by New York-based KKR in March 2004 for $1.5 billion from an investment group that included Bain Capital, the private-equity firm previously led by Republican presidential candidate Mitt Romney. KKR paid $5.78 a share for the bedding maker and took it public two years later for $16 a share. The stock peaked at $17.90 in April 2007 and slumped during the recession that started later that year. It never recovered.

Thursday’s transaction, which is expected to be completed in the first half of 2013, will create cost savings of more than $40 million by the third year, the companies said.

Since 1989, Sealy has traded hands from Gibbons, Green & van Amerongen Ltd. to Clipper Group to Zell/Chillmark Fund to Bain to KKR. Bain led a group buying Sealy in 1997 for $833 million and made more than five times its original equity investment upon selling the company seven years later to KKR, the investment firm led by Henry Kravis and George Roberts.

In June, Tempur-Pedic lowered its full-year profit and revenue forecasts, citing a slump in sales in April and May, amid increased competition. Last year, Tempur-Pedic, which sells some mattresses for more than $9,000, became the biggest publicly traded mattress company by revenue as sales rose 28 percent to $1.42 billion. Sealy operates 25 plants in North America and had sales of $1.2 billion in fiscal 2011.

Tempur-Pedic specializes in non-spring mattresses, making its products with a pressure-absorbing foam, drawing on technology first used by NASA.