The stunt, called "that sofa", uses hidden cameras to film people sitting and interacting with a talking sofa, which uses Joly’s voice.
At first, the sofa is very welcoming and showers the new arrivals with jokes and gifts, but quickly loses interest when other people walk past.
The 30-second and 90-second videos aim to show the neglect that existing bank customers feel when new customers are treated better than them.
These videos are part of M&C Saatchi’s wider 'Goodbye, Hello' integrated campaign, which promotes the two banks’ commitment to fairer banking.
The stunt was filmed at a London shopping centre and Dom Joly directed it through Good Egg. The copywriter was Kieron Roe and the art director was Dominic Moira. The media agency was ZenithOptimedia.
Derek Hemphill, the senior marketing manager at NatWest, said: "This campaign is all about demonstrating how we are putting loyalty and fairness first. The hidden camera stunt with Dom Joly is the perfect way to illustrate how customers feel about the unfair practice of always giving the best deals to new customers."
The videos will go on both banks’ Facebook, Twitter and YouTube channels today. The agency is also planning a homepage takeover of YouTube on the 24 October.
Gabrielle Bell, the strategy director at M&C Saatchi, added: "Digital allows us to push boundaries in banking communications, tangibly demonstrating what the promise to put fairness first really means for NatWest and RBS customers.
"Fairness can be quite an abstract concept, so we have positioned it against the unfair treatment that many people still experience in the form of our fickle and grouchy couch."