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Umpqua Holdings, Oregon’s biggest bank, agreed to pay about $2 billion in stock and cash to buy Sterling Financial, the Spokane-based lender backed by Warburg Pincus and Thomas H. Lee Partners.

Sterling shareholders will receive 1.671 shares of Umpqua stock and $2.18 in cash for each of their shares, the companies said Wednesday in a statement.

That values Sterling at $30.52 a share, or 26 percent more than its close of $24.20 on Aug. 30, when Bloomberg News reported Sterling was for sale.

“With our size, shared cultures and financial strength, our combined organization will be uniquely positioned to deliver value,” Umpqua Chief Executive Officer Raymond Davis, who will lead the combined company as CEO, said in the statement.

Buying Sterling would double Umpqua’s size to about $22 billion in assets and almost 400 branches. Warburg Pincus and Thomas H. Lee, the private-equity firms, each held more than 20 percent of Sterling’s common stock at midyear.

Sterling fell 2.2 percent to $26.55 in regular New York trading Wednesday before the news. Umpqua slid 1.3 percent to $16.96.

Both boards approved the deal, which is to be completed in the first half next year, the banks said.

Davis has sought to bulk up Umpqua over the past two years through mergers and acquisitions. The lender completed the purchase of Financial Pacific Holding in July, and last year bought Circle Bancorp, a six-branch lender in Novato, Calif.

Sterling took $303 million from the U.S. Treasury Department’s Troubled Asset Relief Program, repaid a year ago through a public stock offering. The bank is run by CEO Greg Seibly, who will be a co-president of the combined bank.

Information from Bloomberg News reporters Matthew Monks and Rick Green in New York is included in this report.