The deal is expected to close in the second quarter, an Advent spokesman told Reuters.
Advent won the bidding war for the company thanks to synergies it identified with Connolly, said the report, citing sources.
Last month Advent and Bain Capital teamed up with Danish pension fund ATP to buy payment processing group Nets for DKK17bn ($3.14bn).
The firms beat three other suitors in the final round of the auction, according to a Reuters report.
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