The agency pitched in partnership with the media planning and buying agency Mediaedge:cia and its direct arm, RMG Blackcat.
It saw off competition led by Tidalwave and Partners Andrews Aldridge.
It will be charged with creating a through-the-line campaign to relaunch Bulldog, which specialises in the provision of broadband services, in direct competition with the likes of BT and AOL.
Gregory Thorpe, the head of marketing communications at Bulldog, could not confirm a budget for the advertising drive. BT Broadband spends around £16 million in the UK.
Simon Bolton, the JWT chief executive, said: "Bulldog is on the brink of becoming a super brand in the burgeoning broadband and internet service provider business. We impressed it with our through-the-line offering and we will be delivering on the brief to make it famous fast. This is a fantastic win for us."
Bulldog has around 16,000 broadband customers but also supplies more than 30 BT exchanges through its network in the capital, giving it direct access to its clients.
It is now looking to boost subscriptions through an advertising push scheduled for the autumn, with Bulldog positioned as an emotionally engaging brand.
The campaign, which will have a London focus, will target individuals and small businesses.