Compuware Corp. will be acquired by private equity firm Thoma Bravo LLC in a deal valued at $2.5 billion, following pressure from activist investor Elliott Management Corp. to sell itself.

Compuware holders will receive $10.92 a share, including cash and stock from the spinoff of subsidiary Covisint Corp., representing a premium of about 17 percent to the company’s stock price at the close of trading on Aug. 29, the companies said in a statement today.

The Detroit-based seller of business software spurned an offer in January 2013 from Elliott Management, which owns 9.6 percent of Compuware. Bob Paul, Compuware’s chief executive officer, cut costs and held an initial public offering of Covisint a year ago. Thoma Bravo had been one of the two firms reviewing the company’s finances in preparation for a possible deal, people with knowledge of the matter said earlier this year. The other potential buyer was Vista Equity Partners LLC.

“We can continue to serve our customers in a competitive environment with greater flexibility to take a long-term approach,” Paul said in the statement.

According to the terms of the deal, Compuware investors will receive $10.43 in cash for each share. Including a tax charge and a distribution of Covisint shares valued at about 67 cents, they’ll receive a total of $10.92 a share, although that figure may rise depending on a final deal price for Covisint.

The shares of Compuware climbed 12 percent to $10.50 at 11:57 a.m. in New York.

“Becoming a private company will enable this established market leader to leverage strategic product and other growth opportunities that will take Compuware to the next level,” Orlando Bravo, a managing partner at Thoma Bravo, said in the statement.

Compuware hired Goldman Sachs Group Inc. in 2012 to help it review Elliott’s bid, and the bank also advised on today’s buyout. Elliott made a conditional, non-binding offer to buy the company in 2012 for $11 a share, valuing Compuware at about $2.3 billion. Including dividends paid out since then, Thoma Bravo’s per-share agreement is higher than the earlier Elliott offer.

Jesse Cohn, the portfolio manager at Elliott involved with the Compuware investment, said the deal delivered a 30 percent return for his firm.

“It’s an OK deal,” Cohn said. “From an activism standpoint, I am happy because a lot needed to be done,” such as bringing in a new chief financial officer, taking Covisint public and adding board members, Cohn said.

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