The deal is a 4.5% increase on the ?172million the broadcaster paid for the current deal.
MOTD presenter Gary Lineker said: "It is wonderful news that we have Match of the Day for another three years. It is a flagship programme and it shows how much the BBC values sport and the importance of football."
The rights cover the traditional Saturday evening slot, the Sunday morning repeat, MOTD2 on Sunday evenings and other evenings when Premier League fixtures justify a show.
It also allows MOTD and MOTD2 to be available on the BBC's iPlayer from midnight on Mondays.
Premier League chief executive Richard Scudamore added: "The free-to-air highlights are extremely important to the broadcast reach of the Premier League; allowing the competition and our clubs to be seen by the maximum possible number of fans across the country.
"The BBC has done a fantastic job for fans of Premier League clubs by providing quality coverage and analysis across their programmes.
"We are very pleased to be continuing our partnership with them."
BBC director of sport Barbara Slater said: "With such an amazing season and thrilling finale, Premier League football has never been more exciting and dramatic. We're absolutely delighted that the TV highlights will continue to be available to licence fee payers.
"We've seen audiences for MOTD grow in recent years and the programme remains one of the BBC's best loved and most iconic brands. The new contract will see MOTD celebrate its 50th birthday and extend coverage to the end of the 2015-16 season."