The amount is less than what the two broadcasters had paid out in the last bid – when they forked out a total of £5.136bn to screen 168 games.
Sky will show a total of 128 matches per season, which is two more than under the previous package, while BT will screen 32 games, down from the 42 secured previously.
Five of the seven live packages have now been awarded. Bidding for the remaining two are ongoing.
According to Premier League that the two live packages has attracted “interest from multiple bidders.”
"We are extremely pleased that BT and Sky continue to view the Premier League and our clubs as such an important part of their offering," Premier League Executive Chairman Richard Scudamore said in a statement late Tuesday.
"Both broadcasters are fantastic partners for the Premier League and have a track record of making our competition available to fans across the country through their high-quality and innovative programming.
BT to engage with Premier League on remaining rights
Sky said it is paying 16% less per match, meaning it is now paying £1.193bn per year, down by £199mln.
"We continue to invest in content that our customers value and which complements our strategy to broaden our offer," said Stephen van Rooyen, Sky's UK chief executive.
"Not only do we remain the home of Premier League football but also the home of top quality drama, entertainment, comedy and other sports."
The remaining games – 40 matches per season – can only be awarded to those who have been part of the bidding process.
No single buyer can hold more than 148 of the 200 matches available.
BT on the other hand, is paying £295mln a season for 32 games, also down from the £320mln paid before when it had the broadcast rights to more matches.
Overall, however, it is paying more per game at £9.2mln, compared to £7.2mln per game under the previous deal.
In a statement, BT said the auction is ongoing and that it “will continue to engage with the Premier League regarding the remaining rights".
BT said it has remained “financially disciplined” during the auction process and “remains in a strong position to make a return on this investment through subscription, wholesale, commercial and advertising revenues, especially following the acquisition of EE, which more than doubled BT’s customer base.”
"The Premier League is undoubtedly the most competitive and exciting domestic league in the world, so we're delighted that our customers will be able to continue enjoying Saturday games on BT Sport," said Marc Allera, chief executive of BT's consumer division.