Charterhouse Capital Partners LLP has beat out rival private-equity firms in an auction for education-software provider Skillsoft with a bid valued at more than $2 billion, according to people familiar with the matter.

London-based Charterhouse will fund the acquisition using leverage of around 7.5 times Skillsoft's annual earnings before interest, taxes, depreciation and amortization, or Ebitda, which is about $180 million, according to one of the people.

Advent International Corp., Bain Capital LLC and Berkshire Partners LLC took Skillsoft private in 2010 in a $1.1 billion deal that underscored the reduced ambitions of private-equity firms still hurting from the financial crisis.

In 2012, Skillsoft bought a smaller rival, MindLeaders, in a deal that lifted its debt-to-Ebitda ratio to above six times, according to Moody's Investors Service.

According to Skillsoft's website, the company has provided digital educational content such as videos and e-books to more than 19 million people through its more than 6,000 customers. Its customers include PGA of America and the University of North Carolina Wilmington.

Private-equity firms long have enjoyed investing in education-related businesses. Textbook publisher Cengage Learning Inc. earlier Thursday received court approval for its bankruptcy-exit plan, which will see lenders including Apax Partners LLP, Oaktree Capital Management and KKR & Co. take a majority stake in the restructured company.

Also Thursday, Hellman & Friedman LLC purchased educational-analytics company Renaissance Learning Inc. from European private-equity firm Permira for $1.1 billion.

Write to Gillian Tan at gillian.tan@wsj.com

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