The rebranded product will be in shops from next month and will be supported by a £10m marketing campaign.
The move follows a two-year hiatus from TV advertising for the brand and is part of an agreement forged during SCA Hygiene's acquisition of Charmin from Procter & Gamble in 2007.
The name Cushelle was selected for its sound, which reflects the product's softness, an SCA statement said. The company describes its new koala icon as a "softness magnet".
SCA said the new brand retained Charmin's "friendly, fun, family image" and believed it will retain its appeal for Charmin loyalists.
Emma Heald, brand marketing controller, said: "The brand re-invigoration for Cushelle represents a major investment for SCA and will mark the start of a really exciting period for the brand.
"We are investing heavily in the campaign to make sure we reassure our consumers that our product has not changed, and we'll be using the marketing campaign to drive loyalty to the brand and, ultimately, market share for Cushelle."
Fallon won the consolidated UK Charmin and Velvet advertising account in October last year.
The agency, which already looked after the £3m UK Velvet account, was awarded the business in a head-to-head pitch against Publicis.
Publicis was Charmin's European advertising agency of record, but Fallon was appointed as Charmin's UK agency three years ago following SCA's acquisition of Procter & Gamble's toilet tissue brands.