Potts, a copywriter, and Jex, an art director, were the creatives behind Fallon's "street music" ad for BBC Radio 1 Xtra, which was named the overall winner at the 2003 British Television Advertising Craft Awards.
The move reunites the duo with the agency where they began their advertising career on a graduate placement.
During this initial brief spell with Mother, their script for Batchelors Super Noodles "shirt" helped them win a D&AD Pencil.
They went on to be hired by BMP DDB, but seven months later they were poached by the newly launched Fallon, as the agency's first hirings.
The Mother partner Mark Waites said: "We offered them a job but they went with Richard Flintham and Andy McLeod, first to BMP and then to Fallon. They have been well looked after but finally decided to come to Mother. They're costing us a lot more now."
While at Fallon, Potts and Jex worked on accounts such as Sony, Nandos, Starbucks and most recently on the launch of BBC3.
Jex said: "The past five years at Fallon working with Andy and Richard have been amazing, but we felt we needed a new challenge and environment to keep ourselves fresh.
"Moving to Mother is a great opportunity for us to go and work with equally talented people."