The football rights deal, worth £394m a year, includes the second-tier Uefa Europa League competition.
From 2018 to 2021, BT Sport will have exclusive rights to broadcast all live matches, highlights and in-match clips of both competitions.
The Champions League, a knockout competition between Europe’s best football teams, was broadcast free-to-air on ITV since its inception in 1992, alongside Sky for much of that time, until BT Sport secured a £900m exclusive deal beginning in 2015.
BT Sport said the final of both competitions would still be available to watch for free on social media. BT streamed both finals on YouTube last year in its first year of holding the exclusive rights.
Uefa, the governing body for European football, held a competitive auction for the bids last week.
Last summer BT launched an ad campaign that marketed itself as a more complete alternative to Sky Sports because it broadcast four football competitions: the Premier League, Champions League, FA Cup and Europa League.
Guy Laurent Epstein, Uefa's marketing director, said: "BT Sport has proved to be an innovative broadcast partner, pushing the boundaries and covering the Uefa Champions League and Uefa Europa League in new ways.
"BT have delivered strong audiences in the UK and we are excited about their future plans for the use of social media which will engage a growing fanbase that consumes sport in different ways."