Centrica is to return £1.5bn to shareholders as a result of the sale.
The energy group plans to pay a special dividend of £1bn and launch a £500m share buy-back over the 12 months following the acquisition.
Centrica had short-listed two potential buyers for the AA, the UK's largest motoring organisation. Kohlberg, Kravis, Roberts of the US had also submitted an offer by last Friday's final deadline for bids.
CVC already owns Kwik-Fit.
The buyers said that they would continue to run the AA as an independent organisation and will also continue the AA Motoring Trust charity.
The AA would also continue to perform its public policy role acting as an independent interest group for motorists.
Centrica said that the £1.75bn price tag would result in a "net cash consideration, after adjustments, of approximately £1.63bn".
Roger Wood, managing director of the AA, announced his intention to retire on completion of the sale, which is likely to be in the early autumn. CVC and Permira have confirmed that Sir Trevor Chinn will become chairman of the AA on completion, and Tim Parker will take over as chief executive.