The deal, which was first reported by Reuters, allows Warburg Pincus to fully cash out after backing the Barcelona-based company for the past two years.
The U.S. investment firm launched an auction process during the summer to find a new owner for the business which serves more than 200 airlines including British Airways, Lufthansa and EasyJet.
Warburg Pincus bought Accelya from French private equity firm Chequers Capital in 2017 and quickly tripled its revenues by merging it with Mercator, a Dubai-based travel services group in which the U.S. buyout firm had been an investor since 2014.
Vista Partners, whose portfolio is mostly focused on software companies, was recently vying to buy a majority stake in WPP's data analytics firm Kantar but lost it to Bain Capital.
Its Chief Executive Robert Smith said Accelya was "at the forefront of innovation and positioned to shape the airline and travel industry for decades to come."
Accelya employs 2,500 employees across 24 offices in 14 countries and recently signed a long-term deal as the International Air Transport Association's (IATA) technology partner.
Bank of America and Evercore advised Warburg Pincus on the deal while Vista hired Goldman Sachs and Houlihan Lokey to work on the purchase.
Law firm Kirkland & Ellis and Simpson Thacher served as the legal advisors to Warburg Pincus and Vista, respectively.
By Pamela Barbaglia