Cardinal Financial Corp. said Monday that it had signed an agreement to purchase United Financial Banking Companies, the holding company for Vienna-based The Business Bank, in a cash-and-stock deal valued at $51.7 million.

The Tysons Corner-based company will pay $38.26 per share of United Financial, more than double Monday’s closing price of $18.50.

The deal, which needs to be approved by regulators and shareholders, is expected to close in early 2014.

The Business Bank’s chief executive, Harold C. Rauner, is slated to join Cardinal as a regional president after the deal closes. The Business Bank has eight branches in Northern Virginia and $331 million in assets. Cardinal, the parent company of Cardinal Bank, has 28 branches and assets of $2.9 billion.