The agreement also includes the British franchises' next four home matches live while away matches will be shown on delay.
There is also scope for highlights shows.
The deal itself is not exclusive to ESPN and therefore the WSB is still able to negotiate rights with other broadcasters.
It also means that the British Lionhearts can negotiate a new agreement with ESPN or another broadcaster if they get out of the group stages and make the quarter finals and beyond.
The deal could prove hugely beneficial to the British franchise if London 2012 super heavyweight Olympic champion Anthony Joshua signs for them, as he recently suggested he might, because the broadcast rights would soar.
But even without Joshua, the British Lionhearts already appear a hugely marketable proposition.
In their first ever WSB in what is season three of the competition, the British Lionhearts secured a 4-1 victory over USA Knockouts at The Hangar in Costa Mesa, California.
They are set to face a tougher task against Dolce & Gabbana Italia Thunder this week but the franchise has named a star-studded line-up for the occasion.
London 2012 silver medallists Fred Evans of Wales and John Joe Nevin of Ireland will be fighting for the British Lionhearts as will Andrew Selby of Wales, who is the number one ranked amateur flyweight in the world.
"I am feeling well prepared," said Evans, who will face France's Michel Tavares at Celtic Manor.
"I am not bothered with whom I face, I will box anyone, anywhere.
"It is just great to be back boxing in front of my home crowd in Wales for the first time since I won my Olympic medal.
"It will be great to box in WSB and I cannot wait to get going and get my first win for the Lionhearts."
Evans, Nevin, Selby will be joined at Celtic Manor by Irish light heavyweight Joe Ward and African heavyweight Mohammed Arjaoui as the British Lionhearts look to build on their superb debut win.
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