Intuit Inc. said Thursday that it has agreed to buy Internet banking services provider Digital Insight Corp. for $1.35 billion in cash.

Intuit, which makes the popular TurboTax software, said it will pay $39 per share for Calabasas-based Digital Insight, an 18 percent premium on the company’s closing price of $33 Wednesday.

The acquisition will help Mountain View-based Intuit expand its business beyond tax and accounting software to include online banking services for small companies and consumers, Intuit said.

Intuit said it plans to finance the purchase with existing cash and as much as $1 billion of debt and expects to complete the acquisition in the first quarter of 2007.

Shares in Digital Insight soared $5.30 in early trading Thursday to $38.30.