The new deal sees Sky Group's total rise to 126 games at a cost of £4.176 billion while BT will pay £960 million to show 42 games.
It equates to a cost of £10.2 million per game. The price paid per annum is around £330 million more than analysts’ forecasts.
Both broadcasters have been able to increase the number of live games due to a slight increase in the number included in the packages.
For the Premier League, the new deal represents a 70 per cent increase on the current TV rights deal, which covers the 2013-16 seasons and cost £3 billion or £6.5 million per game.
Live Premier League rights are currently split between Sky and BT, with the former showing 116 matches, with 20 "first picks", and the latter showing 38 matches, with 18 "first picks".
From 2016, Sky will broadcast 126 fixtures a season versus 116 under the existing contract, including live coverage of matches on Friday evenings for the first time as well as its usual Saturday afternoons, Sunday afternoons and Monday evenings.
Jeremy Darroch, chief executive of Sky Group, said: "This is a good result and confirms that Sky is the unrivalled choice for sports fans. We went into the Premier League auction with a clear objective and are pleased to have secured the rights that we wanted.
"Our strong performance across the board gives us financial strength and flexibility. We have a clear plan to absorb the cost of the new Premier League deal while delivering our financial plans."
The new rights will increase BT Sport's coverage from 38 to 42 games, including live Saturday evening matches every Premier League weekend for three seasons.
John Petter, chief executive of BT Consumer, said: "I am pleased we will be showing Premier League football for a further three years and that we have secured the prime Saturday evening slot.
"These new rights will enhance our existing schedule of football, rugby and other international sport, including all the live football action from the Uefa Champions and Europa Leagues starting this summer.
"BT Sport has got off to a strong start, reaching more than five million households and commercial premises, by making itself far more affordable and accessible to sports fans."
The first broadcasting rights for the Premier League were solely bought by Sky in 1992 at a cost of £191 million or £0.6m per game.
That increased to £670 million in 1997-2001 and rose to £1.2 billion in 2001-2004 period. However, the cost of the broadcasting rights actually fell to £1 billion in 2004-2007, with Sky the sole bidder, before rising to £1.7 billion when Setanta was awarded some games for 2007-2010.
Sky and ESPN spent £4.3 billion on the rights in 2010-2013 before the arrival of BT changed the game and almost doubled the cost to £3 billion.
Commenting on today's auction, Robin Clarke, managing director of sports at Starcom MediaVest Group, said: "Once again the broadcast rights for Premier League smashed all previous bids. In fact, throughout this current process nobody predicted it would break the five billion figure.
"This staggering total of £5.136bn not only represents a huge increase (up from £3bn on 2014-16) but is testament to the major priority Sky has given to securing five of the seven packages available from the Premier League.
"While BT will feel they have won a good new slot with the Saturday evening games (and don’t forget they have UCL and Europa league exclusively from next season), Sky has undoubtedly strengthened its hold on the Premier League with the new Friday night games being a further sales window of opportunity alongside Super Sundays and Monday nights.
"As ever, the big winners here are the clubs and the players. The latter will go in to contract negotiations armed with higher demands. Let’s not forget, that £5.136bn is just for UK rights. The rest of the world is still to come on this cycle.
"For Sky though, this seemingly was just too big to lose. Sport again tightens its grip as the crown jewel in live TV viewing."