The agency won the new account after a pitch handled by Oystercatchers. Investec has not worked with a direct marketing agency in the past.
PAA will be responsible for helping to expand the financial brand's private banking division with a big focus on loyalty marketing.
Until now, the bank has relied on press and search marketing, as well as sponsorship deals, to boost its profile. Gravity will continue to handle the brand's advertising.
Last year, Investec struck a deal with the England and Wales Cricket Board to sponsor Test match cricket.
Denese Edgar, the head of marketing at Investec Specialist Banking, said: "PAA pushed us out of our comfort zone. Our aim is to change private banking and turn it on its head. We appointed PAA to help us break the mould and produce provocative ideas."