The deal is worth £179.7m and will cover the Saturday programme, its Sunday morning repeat and Match of the Day 2 as well as highlights shown during the week.
Both shows will also be available on iPlayer after midnight on Mondays, with the broadcaster allowed to show a maximum of 30 minutes from any match.
It is not known if any of the other broadcasters such as ITV bid for the highlights package.
The extension means that Match of the Day will celebrate its 50th birthday during the second half of next season.
The current deal was due to end at the end of the 2013-14 season.
The tie-up comes just days after the BBC signed a three-year deal with the Football League ending rumours that the Saturday highlights show would be cancelled after “budget decisions” forced several Christmas programmes to be cancelled.
The Premier League is in the process of auctioning its TV rights, said to be worth more than £3.5bn, for the next three years. Deals for domestic live broadcast rights, which are currently held by BSkyB and ESPN, are expected to be concluded by mid-July.
The last auction was held in 2009 and was worth around £3.5bn, making the Premier League the world’s richest domestic football tournament.