The ads, which break on 1 October, maintain the creative idea that was conceived by David Abbott 17 years ago.
In "brains", the traditional red background associated with The Economist's advertising runs without the brand's logo. Instead, it carries an image of the character Brains from the television series Thunderbirds.
Other ads use straplines including "voted best mortgage provider 2004" and "you can so tell the people who like don't read The Economist".
Jacqui Kean, the brand marketing manager, said: "A key component of the advertising is its wit. People engage with the campaign and enjoy the intellectual challenge."
The campaign will run in more than 1,000 locations in major UK cities, including a site outside Chelsea Football Club's Stamford Bridge ground, which will carry the "you don't have to be a billionaire to buy success" execution.
Media planning and buying is handled by PHD through Outdoor Connection.
The ads will appear as six-, 48- and 96-sheet posters, as well as on cross-tracks.
Matt Doman and Ian Heartfield were the creative team behind "voted best mortgage provider", "you can so tell the people who, like, don't read The Economist" and a third ad, "the chaff". "You don't need to be a billionaire to buy success" was written and art directed by Tim Riley, as was another ad, "pay and display". "Brains" was created by Tony Hardcastle and Mark Tweddell. AMV's joint creative directors, Paul Belford and Nigel Roberts, created "stop having to remind people who you are".