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The move means that from next season, BT Sport will boast coverage of the FA Cup, the Scottish Premier League, the Europa League and the German Bundesliga, as well as showing 38 matches from the English Premier League.
"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," said Marc Watson, chief executive of BT television.
"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."