Almost one million consumers have downloaded the BT Sport app since it was launched at the start of August 2013.
Speaking at the Royal Television Society, BT TV Chief Executive Marc Watson said the app is proving "a major hit" with users, and the million-user milestone should be passed at some point in September.
He claimed that the trend for people watching TV content online – whether via a PC, Mac or a mobile device – is growing. And as such, broadband will increasingly be "an important platform for television".
Mr Watson said television "is changing thanks to broadband" and that transformation will only become more dramatic as customers move to faster fibre connections.
"The BT Sport App has proved to be a great success with our customers," he stated.
"More than a million homes will have soon downloaded the App and, whilst many of those can also watch via their TVs, there are literally hundreds of thousands of people who have chosen to watch exclusively online."
Mr Watson commented that BT Sport is "as much about broadband as it is about TV".
He said the firm is "proud as punch" of its channels, which offer live Barclays Premier League football and Aviva Premiership rugby union among other sporting content.
But Mr Watson said BT Sport 1, BT Sport 2 and ESPN exist first and foremost to entice new customers to take out BT broadband deals, and to encourage existing customers to remain loyal.
"Some people think we are trying to win TV customers off Sky but the truth is far more nuanced," he stated.
"There is lots of room for both Sky and BT in the TV space but we are rubbing elbows in the broadband market."