The new deal with Sky Sports, BT Sport, Amazon Prime Video and BBC Sport will run from 2022 to 2025.
The current £4.7bn deal, agreed in 2018, represented a 10% drop in value.
The Government has approved the deal "in principle" with an "exclusion order" under the competition act, which allows the league to renew without its normal tender process.
"In light of the damaging impact of the Covid-19 pandemic throughout the English football pyramid, the Premier League was able to demonstrate to Government exceptional and compelling reasons for the Exclusion Order," the league said.
As part of the new deal, BT Sport say that to help with the fixture congestion, they will change their Saturday lunchtime game to an evening slot when teams involved have played in Europe on the previous Wednesday.
Much better than watching intermittent streams.