Isobel beat M&C Saatchi, DraftFCB and Creature in a pitch handled by the intermediary Oystercatchers.
The agency will create a campaign for the brand, which will include TV and online, to launch in April.
Beta previously handled the business, having been appointed in July 2009, and launched a campaign starring Barbara Windsor.
Maxus will continue to handle media planning and buying for the brand.
Michael Saunders, the managing director of Jackpotjoy, said: "We have been tremendously impressed with Isobel's creativity and its shared ambition for the brand."
Paul Houlding, the chief executive of Isobel, said: "Jackpotjoy is a great brand and we've got some cracking creative campaigns up our sleeve. We look forward to a successful long-term relationship."