The sale is expected to complete in the first half of 2018.
Netherlands-based TMF Group, which provides financial, legal and administration services for multinationals, said this month it planned to raise 340 million euros from a London share listing in November, aiming to reduce its debt.
A source familiar with the matter said that TMF had been expected to have a market valuation of between 1 billion pounds and 1.3 billion pounds had the listing proceeded.
It would have been one of the biggest initial public offerings on the London exchange this year.
TMF Group, which has been owned by DH Private Equity since 2008, has not disclosed its debt level, but it reported a loss of 37.8 million euros for the first half of 2017, up from a loss of 28.7 million euros in the first half of 2016.
It said on Friday that the deal with CVC would allow it to capitalise on "significant" future growth opportunities.
In June CVC Capital raised 16 billion euros for its latest fund for private equity investments in Europe and North America.
Low interest rates and cheap debt have contributed to a boom in private equity fundraising since the financial crisis, supported by investors' thirst for high-yielding alternative assets.
A spokeswoman for TMF said the company had also dropped plans to relocate to London after listing.
She declined to comment on when talks began with CVC.
TMF Group was advised by Goldman Sachs International and HSBC Bank.
(Reporting by Noor Zainab Hussain in Bengaluru; additional reporting by Esha Vaish in Bengaluru, Bart H. Meijer in Amsterdam and Dasha Afanasieva in London; Editing by Edmund Blair and Susan Fenton)
By Noor Zainab Hussain