RedPrairie, a maker of business software, on Thursday said that it had agreed to buy Scottsdale-based JDA Software Group Inc., a maker of supply-chain management software, for about $1.9 billion in cash.

RedPrairie, a privately held company based near Atlanta, is paying $45 per share for JDA Software.

Shares of JDA jumped $6.65, or 17 percent, to $44.80 in afternoon trading, indicating that investors expect the deal to go through at the agreed-upon price.

The price was a 33 percent premium to JDA’s stock price on Oct. 26, the day before rumors of the deal started leaking out, RedPrairie said, and 16 percent above JDA’s all-time high.

The companies expect the deal to close by the end of the year.

The combined company will have annual revenue of more than $1 billion and will be led by Hanish Brewer, the CEO of JDA. The CEO of RedPrairie, Michael Mayoras, will stay on the board.

“JDA’s heritage of pioneering market-leading supply chain planning, merchandising and pricing solutions is a perfect strategic fit with RedPrairie’s heritage in warehousing, workforce management, store operations and e-commerce,” the companies said.

Separately, JDA reported third-quarter net income of $11.1 million or 26 cents per diluted share, down 34 percent from $18.3 million, or 43 cents per share, in the third quarter of 2011.

Revenue was $164.5 million, down 5 percent from a year ago.