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Robert F. Smith, chairman and chief executive of Vista Equity Partners.Credit Chester Higgins Jr./The New York Times

HONG KONG — Vista Equity Partners agreed on Sunday to buy Solera Holdings, which provides software to insurance and car companies, for $6.5 billion, including net debt.

Vista, a private equity firm based in the United States, would purchase all of the outstanding Solera shares at $55.85 per share in cash. The price reflected a premium of 53 percent over Solera’s closing share price of $36.39 on Aug. 3.

Talks were reported to have stalled last week over Solera’s valuation expectations. Its board of directors has now approved the acquisition and recommended that stockholders vote in favor of it.

“This transaction delivers immediate compelling value to our stockholders and represents a pivotal milestone for Solera in partnering with Vista,” Tony Aquila, Solera’s founder and chief executive, said in a news release. “It not only recognized our innovative company and talented employees, but also provides us with the optimal flexibility to proliferate our world-class solutions and services for our customers.”

Robert F. Smith, founder and chief executive of Vista, said, “Solera is incredibly well positioned for the next fifty years.”

Solera, based in Texas, provides services to companies in more than 75 countries.

Vista, which is known for its unconventional management tactics, has focused its investments on software and data companies. In February, it acquired Automated Insights, which creates automated articles about companies’ financial results for The Associated Press. In November 2014, it announced it would acquire Advanced Computer Software Group, a British health care and business software maker, for 725 million pounds, or about $1.14 billion.

Koch Equity Development and an affiliate of Goldman Sachs are partners with Vista on the Solera acquisition.

The deal is expected to close by the first quarter of 2016.