The deal includes ESPN and ESPN America channels and their live sports rights including the FA Cup, Clydesdale Bank Scottish Premier League, UEFA Europa League, and the German Bundesliga.
Chief executive of television BT Retail Marc Watson said: "We are delighted to have reached agreement with ESPN for the acquisition of their UK channels business and that we have been able to add some exciting new sports rights to the ones we already have.
"The FA Cup, Scottish Premier League and Europa League rights will allow us to offer customers of BT Sport even more quality live football, including our first games from the Scottish top flight and our first European competition rights.
"There will also be the best of US sports available courtesy of this deal, which will further broaden the appeal of BT Sport."
Managing director, ESPN - Europe, Middle East and Africa Ross Hair added: "We could not be more proud of the TV channels built and nurtured by our talented team over the past four years.
"The value of that hard work is reflected in this deal with BT and the continuation of ESPN on television screens across the UK and Ireland.
"The same passion, commitment and innovation will be at the heart of how we develop our strong digital media business into the future."
After the deal completes on July 31, 2013, BT will continue to run one branded ESPN channel which will operate under the BT Sport TV umbrella.
BT will also show NCAA College Basketball, NCAA College Football and NASCAR, which are currently shown on ESPN America.
The channel will be broadcast from Stratford's Queen Elizabeth Olympic Park, where BT Sport is situated.
BT Sport recently made waves with the purchase of 38 live Barclays Premier League matches - including 18 of the top clashes for the next three seasons.
ESPN will continue to operate and own its own digital media businesses, websites and broadband streaming service.