Goulborn has been offered what he described as his "dream job", sales and marketing director at Ipswich Town FC, which he has supported since childhood.
Rise's co-founder, the former Optimedia managing director Simon Mathews, will continue to run the agency along with the third partner, John Wigram.
Mathews intends to recruit a replacement for Goulborn, who previously worked at Saatchi & Saatchi and MediaCom, as well as a data and research expert.
Goulborn, who is reunited at Ipswich with former Saatchis colleague Derek Bowden, now the club's chief executive, said: "The dilemma was that Rise was going well and I'd put a lot into the launch, but I knew for sure that the Ipswich chance wasn't going to come along again."
Mathews said: "It's a shame because we set the business up together but he's supported Ipswich through thick and thin. We'll move on."
Goulborn will relinquish his stake in the agency, which has clients including Metro newspaper and Reckitt Benckiser.
Mathews added: "While Rise is definitely sad to see him, go we have to accept that we are part of an industry that can not compete with the lure of a local football club for a fan as dedicated as Andrew."
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