ServiceMaster stockholders will get $15.625 in cash for each outstanding share, a premium of about 16 percent over Friday's closing price of $13.47 on the New York Stock Exchange.
Clayton will also assume about $800 million in debt, said ServiceMaster spokesman Steve Bono.
ServiceMaster stock was up on the news. The company has 303 million shares outstanding.
On completion of the transaction, Clayton's operating partner, George Tamke, will become chairman of the ServiceMaster board. Patrick Spainhour will remain chief executive.
ServiceMaster's businesses also include American Home Shield warranties and the Merry Maids cleaning service, as well as drain cleaning and furniture repair operations.
The company, which was founded in 1929, competes with Scotts Miracle-Gro Co.'s
Shareholders will vote on the deal at a special meeting during the second quarter.
Including Monday's gains, ServiceMaster shares have gained 27% since November 28, when it said it was putting itself up for sale amid higher costs and weak customer retention.
Last month, it said retention rates had started to improve as it used direct mail and other marketing efforts to go after new customers, putting less emphasis on telemarketing.
The company still plans to move its headquarters to Memphis, Tennessee, from Illinois by early July, Bono said.
"If this deal is looking to close at the end of the second quarter, early third quarter, that move would be substantially done before it closes," Bono said.
Morgan Stanley and Goldman Sachs acted as financial advisers to ServiceMaster.