"Sky has chosen to pay £1.193bn per annum under the terms of the new deal", the company said in a statement, "down £199m per annum, a 16 per cent cost reduction per game versus the current agreement".
BT claimed the other package to have been sold so far, switching from its current 5.30pm slot on Saturdays to 32 games at 12.30pm.
Having secured one package of 42 matches in the current deal, and the rights to all United Kingdom broadcasts of the Champions League, BT Sport said it had "remained financially disciplined" in the auction for the 2019-22 rights.
The Premier League still has two packages with a combined 40 matchday broadcasts remaining to be sold.
Considering its success in simultaneously broadcasting entire Champions League matchday programmes, BT must be considered the favourite for at least one of the two remaining packages.
Sky have paid £3.579billion for their rights, with BT forking out £885million. BT won one package and will pay £295 million per season.
In other words, to get the same cash, the Premier League have given broadcasters and extra 32 (168 v 200) matches of the maximum 380 games per season. It also claims to have secured the best slots including Saturday tea time matches, Super Sunday, Monday Night Football and Friday Night Football and for the first time, Saturday evening matches.
Elliott, the US hedge fund best-known for its activist campaigns at companies, including forcing bidders to pay more during takeovers, has also been stakebuilding in Sky recently and lifted its interest to 1.99 percent last week.
Miles acknowledged the league had listened to fans' groups on capping ticket prices for away supporters but said it should go further.
Expanding its coverage, the Premier League will allow Sky Sports to broadcast 8 "Saturday 20:00 PrimeTime" matches for the first time.
Marc Allera, CEO of BT's Consumer, said: "BT Sport is enjoyed by over five million households and pubs and clubs across the UK". But reports suggest both Sky and BT Sport have become increasingly financially stretched to justify pushing the price higher.
The companies commented that they had taken a "disciplined approach".
Commenting on the reduced £3.579bn the company is paying for its four prime packages, Stephen van Rooyen, Sky's United Kingdom chief executive, said they had taken a "disciplined approach".
However, the auction is still ongoing with two of the seven packages still yet to be decided, leaving open the possibility of a bid from one of the digital giants such as Amazon.
"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", said Premier League executive chairman Richard Scudamore in a statement.